West Ham took the lead in the second minute when Diafra Sakho headed in from Dimitri Payet's free-kick but they were pegged back by Zlatan Ibrahimovic before the break.
Keeper Darren Randolph was man of the match for the Hammers who had their opportunities to get a winner but Bilic was content overall.
"It might have been more but it is a great point for us, especially as we played well. I have to praise the players, who showed character, commitment and quality, especially in the second half," he told reporters.
"In the first half, when we scored, we were a little bit afraid because we were winning at Old Trafford and then until they scored we lost too many balls.
"In the second half, we told the players to go up on them and I was very pleased with how we played. You can't attack here all the time.
"They tried to press when they lost the ball and if you get out of that, there is a lot of space. We were using that really well in the second half."