But again Bilic's side have so far failed to perform yet again and find themselves trailing to a goal from former Italy and Juventus forward Fabrizio Miccoli in the 14th minute.
West Ham's midfield has looked pedestrian all half and they allowed a simple ball over the top to find Liliu who burst through and provided the cross for Miccoli to score at the end of a quick counter-attack.
Bilic had called on his players to keep cool in the intense Maltese heat, wary that the hosts would try every trick in the book to claw their way back into the tie.
But his wise words fell on deaf ears as his players allowed themselves to become embroiled in needless, petty rows throughout and were clearly wound up by the antics of Birkirkara.
Instead of letting their class do the talking the likes of Mark Noble, Joey O'Brien and James Tomkins rowed on several occasions and it resulted in last week's hero Tomkins being shown a straight red card just before half-time.
It leaves the game all square at 1-1 on aggregate but the Hammers are staring a potentially embarrassing early exit from the Europa League in the face.
The Hammers only needed to look at the last time they played in Europe for a warning on how short and not so sweet it can be.
This is the first time in nearly a decade that the Hammers have played in European competition.
The last time was in the 2006-07 season when they were knocked out of the Europa League's predecessor the UEFA Cup by Italian side Palermo 4-0 on aggregate.