The Reds appeared destined to be held to a goalless draw heading into the closing stages of a meeting with their Merseyside rivals.
Divock Origi was, however, to snatch all three points after Jordan Pickford flapped at a wayward shot from Virgil van Dijk that looped onto the Toffees’ crossbar.
In the heat of the moment, Klopp raced from his technical area to celebrate and found himself embracing his goalkeeper near the centre circle.
He was charged with improper conduct and fined, while also apologising for his actions, but Alisson admits those inside the Anfield camp have no regrets at how they acted.
"It was at the end of the game, I was celebrating. Generally, I prefer not to celebrate too much so I can concentrate on the game and stay level-headed but the goal came at the end of the game so I could let it all out.
"I ran to the middle of the field and did my usual celebrations, pointing to the heavens, thanking God, and then I looked to one side and I saw Jurgen and I thought, 'What is he doing?' It was a great moment and I gave him a big hug.
"I appreciate it wasn't the correct thing to do and he has been punished for that - but it was worth it."
Alisson’s efforts against Everton helped Liverpool to a priceless win, as he secured another clean sheet.
He followed up that display with another impressive one against Napoli in midweek, with one stunning late stop seeing the Reds to a 1-0 victory and a place in the Champions League last 16.
"A save at the end of the game is always great and you feel you have contributed to the game," added the South American on his European heroics.
"Of course, an important save in the first minute is as important as a save in the last minute but for the fans it's the closest thing to scoring a goal in the last minute, like we did in the derby against Everton.
"But I only managed to make that save with the help of my teammates' contribution and thank God we got the victory."
Alisson will be hoping to secure another shut out on Sunday when unbeaten Liverpool welcome old adversaries Manchester United to Anfield for an eagerly-anticipated Premier League encounter.