West Ham's Sam Byram and Manchester City's Kevin De Bruyne in action
They were seeking to secure a positive result to take back to the Olympic Stadium as they seek to progress to the group stages of the competition.
West Ham's Sam Byram receives instructions
Things did not go to plan though as a brace from Matic Crnic saw the home side grab a slender advantage to take into the second leg.
Byram played all 90 minutes in the game, and says he enjoyed his first taste of European football despite it ending in defeat.
“We’re disappointed to lose here as we thought we would be coming away with a result,” he told the club’s official website.
“It was my first experience of the Europa League and I really enjoyed that. It is just a shame about the result.”
West Ham players pose for a team group photo before the match
The pressure is now on the Hammers to secure a positive result in the second leg and progress to the group stages.
They were clearly surprised by the quality that Domzale showed, with this result one that shocked many to say the least.
The pressure will be on them to right it at home as a result, especially as it is their first game at the Olympic Stadium, and it will be interesting to see if they can handle that.
West Ham players dejected after the game