The Hammers brought the curtain down on their 112-year stay at the Boleyn Ground, and it ended in fitting fashion as Winston Reid's winner capped off a late comeback to lift West Ham up to sixth in the table.
The win also denied Manchester United the chance to move into the top four, and Bilic believes that it had all the hallmarks of a game that will live long in the memory.
"It was big pressure for us. We have had a great season and I told the guys however it finished in the last few games it has been a great season for West Ham," he told Sky Sports News.
"We were under pressure still, we didn't want to lose our last game. We just wanted to win it and this was a win of character. We didn't stop believing. We knew they were highly motivated because they could have leapt above Manchester City.
"We totally deserved it. It was a great night, it is history, not just a game, it is against them, fighting for Europe, late night game. All the boxes you need for a special type of game was tonight."
West Ham will now be guaranteed European football in their first season at the Olympic Stadium if they beat Stoke City on the final day of the campaign.