The Hammers progressed to the fifth round at the Reds' expense as Angelo Ogbonna headed home in the last minute of extra time, much to the delight of his manager
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."