The Hammers needed a 90th-minute goal from defender James Tomkins to claim a first-leg advantage to take to Malta next Thursday, despite dominating most of the game.
Birkirkara set up very defensively and tried to restrict West Ham’s offensive bursts, a tactic that worked well until Tomkins bundled the ball in from a corner as the game moved into added time at Upton Park.
“It is more relief because we scored at the end, but I think we played well, especially the first half,” said Bilic.
“We didn’t play really quick, but quick enough against this type of opposition. They are a decent side, they are not, with all respect, Real Madrid, but they are not like the team from Andorra or San Marino. They can make your job more difficult.
“It was okay for this stage of pre-season, the crosses were not brilliant, but then we created three or four chances, were a bit unlucky with hitting the post, but also we did not have the quality.
“We lost a bit of patience in the second half and were just playing square balls and lost a bit of strength and freshness, which is impossible to have at this stage of pre-season.”
But Bilic was pleased to see his side battle through their lack of match fitness and snatch victory, and even though they are behind, he expects Birkirkara to use similar tactics on home turf next week.
He added: “In the last 15 minutes we raised the tempo and put the pressure on them, to score the goal from a set piece, which we fully deserved.
“We are well organised and are working hard for each other, but in the last third of the pitch, well, there you need some extra quality.
“We played without some players who are extra special, and with more freshness for these players and the ones who are missing, we will get that. I am really happy that I have a group that I can work with and will listen, to improve, which is what makes me optimistic.
“It is not job done, of course. They will probably play the same way in Malta, and will wait again for some long ball, some mistake or counter-attack, but we are quite confident.”