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.”
A goal apiece from James Tomkins and Luka Milivojevic handed Crystal Palace a crucial 2-0 win over Huddersfield at the John Smith's Stadium on Saturday evening.
Manchester United bounced back from their Champions League exit as they beat Brighton 2-0 at Old Trafford on Saturday night to reach the FA Cup semi-finals.
Tottenham reached the FA Cup semi-finals after they cruised to a 3-0 victory over Swansea in their quarter-final clash at the Liberty Stadium on Saturday.
Premier League basement club West Brom squandered the lead as they suffered a 2-1 defeat to Bournemouth at the Vitality Stadium on Saturday.
Chesterfield boss Jack Lester felt his side were unlucky not to claim all three points after their 1-1 draw at Cheltenham.
New Swindon manager Phil Brown revelled in his side's victory at Cambridge in his first game in charge.