Angelo Ogbonna's injury-time header gave the Hammers a 2-1 win in the fourth-round replay at Upton Park, punishing Liverpool for their wastefulness in the process.
The Italy international's first goal for the club sent the Upton Park faithful into raptures, celebrating a victory that looks set to be a defining memory from their final season at the famous ground.
But Bilic believes the triumph could take up an even loftier position in the West Ham pantheon, with a fifth-round tie with Blackburn Rovers beckoning.
"It was for me a really great game of football and it is like a classic FA Cup tie. It is going to go into history of West Ham's greatest games," he told BT Sport.
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"I know it is only for the last 16 but this is against Liverpool, a late night kick-off, the last season at Upton Park, a great game and a goal in the last minute – I think we deserved it.
"I am very proud of the guys. They left their hearts on the pitch and I am very, very proud of them."
Bilic was forced to replace defenders Winston Reid and Joey O'Brien, along with midfielder Cheikhou Kouyate, due to injury – a run of changes that saw winger Michail Antonio deployed at right-back having opened the scoring on the stroke of half-time.
This collective effort in adversity pleased Bilic, who reserved special praise for his match-winner.
"All of them had a really good game and also the substitutes," he said. "Because of injuries we had to put some players not in their natural positions – Michail Antonio did a great job as a right-back.
"I just told Angelo the goal came as the cherry on the pie of his game because his game was simply magnificent as a centre-half and he deserved to score that goal in the dying seconds of the game.
"And what a goal, it was a great goal also."