The club narrowly missed out on a trip to Wembley after being held by a late goal against Manchester United at Old Trafford before losing 2-1 in the replay at Upton Park.
A 3-1 win over Watford last time out kept the Hammers on course for European football, a quest they resume against West Bromwich Albion this weekend.
The Irons may yet enjoy their best ever season in the Premier League era.
But Bilic still faces a major clear out this summer, here's who needs to go and why.
The versatile Irish defender has surely come to the end of the road in his Hammers career after another injury ravaged season. The 30-year-old has not made a single Premier League appearance this season and has featured only once in the FA Cup and twice in Europa League qualifying in pre-season.
With the club having signed young right back Sam Byram and with James Tomkins and Michail Antonio also able to play there, O'Brien will undoubtedly be looking for a new club this summer, most probably in the Championship.
The Canadian centre back joined West Ham with a big billing from then manager Sam Allardyce back in January 2015. Henry is still only 23 and won rave reviews after a brilliant debut on loan at Blackburn Rovers.
But he was injured afterwards and to date has only played once for West Ham since, in Europa League qualifying in pre-season where his mistake proved costly.
With the likes of Winston Reid, James Collins, James Tomkins and Angelo Ogbonna in front of him, Henry is also competing against the fast emerging talents of Reece Burke and Reece Oxford as well as versatile midfield star Cheikhou Kouyate who has often filled in at centre back.
Like Henry, Hendrie signed back in January 2015 but did not officially arrive at the Hammers from Scottish side Hamilton until last summer for the start of Bilic's reign.
Hendrie earned rave reviews in the development squad and on a brief loan spell at Southend United.
But the Scottish Under 21 international has yet to feature for Bilic in any competition despite being frequently named in matchday squads.
Aaron Cresswell is the firmly established first choice left back and with homegrown Hammer Lewis Page emerging through the Academy, it wouldn't be a surprise to see Hendrie leave, although some back-up would be needed for the left-hand side.
The on-loan Barcelona midfield star was a revolution when he first joined West Ham in the summer of 2014 under Sam Allardyce. He was winning the man of the match award every week but his form dipped alarmingly in the second half of last season as the Hammers dropped from third place on New Year's Day to 12th by the season's end.
His loan was renewed by Bilic upon replacing Allardyce despite the former Arsenal star being out with a long-term injury.
But he has failed to recapture anything like his best form since and has rarely featured in the side this season. The Hammers have already sealed the signing of Borussia Monchengladbach midfielder Havard Nordtveit as Song's replacement, as reported by the Daily Mail.
When Victor Moses signed on loan for the Hammers it was seen as something of a coup. In reality the former Crystal Palace star, who signed a new long-term deal at parent club Chelsea before arriving on loan in East London, has showed all the inconsistencies which have held back his progress in recent years.
Moses has showed flashes of the brilliance that has seen him end up at one of the richest clubs in world football. But he has only made 16 appearances for Bilic and scored just one goal, away to Manchester City.
Moses will return to Stamford Bridge this summer as the Hammers aim for bigger and better with their move to the 60,000 seater Olympic Stadium.
Moses' fellow Nigerian arrived on loan in January after the exit of Croatian forward Nikica Jelavic. Emenike has scored twice, in the same FA Cup game at Blackburn Rovers but has flattered to deceive since.
He has worked tirelessly, though, and offered strength, pace and a good team ethic. He was definitely an upgrade on Jelavic but the Hammers have confirmed they will be in the market for one or two top class strikers this summer and his loan will not be made permanent.
It all started so well for Valencia at West Ham with some explosive goals and his partnership with Diafra Sakho pushing the Hammers as high as third last season. But injuries have restricted him to 48 appearances and just eight goals in two seasons.
He is in and out of the side under Bilic and has shown a petulant attitude on a number of occasions when substituted recently.
For £12 million West Ham would expect more and while he offers genuine pace, Valencia may be a casualty of the club's search for two stellar forwards this summer.
Had his worst game in a West Ham shirt in the club's huge FA Cup quarter-final replay against Manchester United earlier this month which left the club's fans seething. Expect any bid of over £7 million to lure him away.