West Ham players pose for a team group photo before the match
Slaven Bilic's side put in an abject performance in what was their first competitive game of the season and were lucky the deficit was not even worse.
Bilic was actually banned from the touchline following his dismissal at the same stage of the competition last year against FC Astra.
The Hammers went 1-0 down on 10 minutes when the referee adjudged Havard Nordtveit had handled in the box and awarded a penalty.
Mark Noble restored parity from the penalty spot but West Ham went on to concede in the second half, failed to threaten the Domzale goal at all and could have lost by more.
But how did the players rate?
NK Domzale's Gaber Dobrovoljc in action with West Ham's Andy Carroll and Adrian
Adrian - 8
Some felt the enigmatic Spaniard could have done better with Domzale's second and many felt Darren Randolph should play as he is West Ham's go-to cup competition goalkeeper.
But if it wasn't for Adrian West Ham would be staring another early exit from the competition in the face after he pulled off a fantastic last ditch double save to deny Domzale a 3-1 lead going into the second leg.
Domzale's Alvaro Brachi and West Ham's Michail Antonio in action
Antonio - 3
Poor Antonio was like a fish out of water. He was obviously told to bomb on but in doing so left gaping holes at the back which Domzale exploited.
He is not a right back and it is a mystery to most West Ham fans why Bilic persists playing him there. The Hammers are also losing his power, pace, skill and finishing at the other end of the pitch.
Was subbed for Quina late on.
NK Domzale's Axel Maraval concedes a penalty against West Ham's Winston Reid
Reid - 5
Winston Reid should be the one calling the shots at the back, organising things, helping Antonio and Byram. But he looked out of sorts, much like he did towards the tail end of last season.
Showed bravery to win West Ham's penalty but his all round game was poor by his high standards and it was reflected in the performance of the back four as a whole which for want of a better word was nothing short of shambolic.
Nordtveit - 4
New signing is a central midfielder by trade but can operate at centre back and full back. Judging on this performance West Ham will be hoping he won't have to fill in there much during his time in East London.
The Norwegian started quite well but gave away the penalty and did not do enough to close the Domzale attacker for their second goal, giving him far too much time and space to pass the ball past Adrian.
He also kept hitting long hopeful balls forward which rarely found a West Ham player. Must do better and probably will when he plays in his proper position.
West Ham's Sam Byram receives instructions
Byram - 6
Considering he hasn't played for the Hammers first team much since his debut against Manchester City back in January - and given he was another player playing out of position at left-back Byram did ok.
He always looked uncomfortable as a right-footed player playing on the left but was actually one of West Ham's better players.
His brilliant pass over the top put Carroll in and the striker should have done much better. But like Antonio is not a right back, Byram - who is a right back - is not a left back. Bilic would have been better served playing Byram and Antonio in their natural positions and using youngster Lewis Page at left back.
West Ham's Sofiane Feghouli in action against Domzale
Feghouli - 7
Probably West Ham's best player on the night, but that's not saying much, and he was far from outstanding.
The Algerian showed his skills, pace and willingness to attack defenders. He also showed that if West Ham can get it together he could weigh in with a fair few assists for the likes of Andy Carroll with his superb crosses from the right hand side.
Not vintage Kouyate
Kouyate - 4
An unusually poor game from one of West Ham's most important players. Continuously gave the ball away or overran it and left big gaps through the centre where he would normally be picking up loose balls or breaking up attacks.
West Ham will need him back to his best if they are to function effectively in the way Bilic wants them to play this season.
West Ham's Mark Noble scores their first goal with a penalty
Noble - 6
Tried to grab the game by the scruff of the neck and scored the penalty which gives West Ham hope for the second leg.
But Noble was pretty ineffective and like Kouyate just could not get to grips with the opposition.
Looked a bit off the pace too.
My bad: Pedro Obiang
Obiang - 4
Hammers fans have been desperate to see more of Obiang after he was used sparingly by Bilic last season. The classy player got his chance against the Slovenians but didn't take it.
He turned in a poor performance overall and should have done better with a couple of efforts inside the box.
Valencia - 4
Fast becoming the new Modibo Maiga, Enner Valencia needs to buck his ideas up if he is to rescue his West Ham career or - as rumoured in recent weeks - secure a move to the likes of Swansea City or Lazio.
He did take on his man a few times but seemed intent on beating the same player five times before doing anything worthwhile.
He wasn't caught offside as much as he usually is, though, so I guess that is a plus.
West Ham's Andy Carroll reacts
Carroll - 5
Worked hard, as he always does, and got in behind a couple of times but finish was lacking on each occasion.
Carroll is a major asset for West Ham but when it isn't working or flowing for Bilic's side he doesn't offer anything like the pace or movement needed to be successful in the modern game.
Carroll should be West Ham's Plan B and the club clearly feel the same with the hunt on for two top class strikers.
Quina walks off the pitch after West Ham's defeat
Quina - 5
Only on for 10 minutes as a replacement for Antonio and looked too lightweight against an aggressive and physical Domzale side.
The young Portuguese star is just 16-years-old and clearly has ability for the club to thrust him straight into action after he was signed earlier this summer.
Wasn't on long enough to properly judge but showed willingness to get on the ball which will go a long way with West Ham fans.