The hosts looked like they would cruise to victory when they were awarded a 14th-minute penalty which would have added to Trent Alexander-Arnold’s shot which deflected in off Fikayo Tomori.
But Mohamed Salah missed from the spot for the first time in 18 attempts, dating back to Huddersfield in October 2017, and Ante Rebic and Brahim Diaz scored within two minutes of each other just before half-time.
Another comeback – although not as significant or as difficult as their 2005 Champions League final achievement from 3-0 down – against the Serie A side was required and Salah provided the momentum with his 72nd goal in his 100th Anfield appearance and Jordan Henderson’s first goal in the competition for seven years clinched victory.
Asked if the game was everything he had hoped for, with a full crowd back in to see a European fixture for the first time since March 2020, Klopp said: “Nearly 100 percent because it was a brilliant game.
“Very exciting and very entertaining with 10-15 minutes where we lost a little bit of the plot or whatever and were not compact any more.
“We got carried away with our own football and complicated matters. They scored two goals and then we played again good football and scored two wonderful goals.”
This was the first time outside of the two finals in 2005 and 2007 that the clubs had met.
While Rafael Benitez had to make significant changes in the dressing room of Istanbul’s Ataturk Stadium over 16 years ago, Klopp was satisfied with the way the game was going as he walked down the tunnel at the break.
“I wasn’t angry at all. I cannot celebrate 30 minutes and then for 15 minutes be angry or whatever,” he added.
“We saw the last five minutes [of the first half] coming so we tried to get the message across but we couldn’t because of the outstanding atmosphere in the stadium.
“We lost the ball in the wrong moment. We started getting a bit complicated. If we are not organised then they just pass the ball through the gap.
“I was waiting for half-time and we could sort it and we didn’t have that problem anymore.”
Milan coach Stefano Pioli was disappointed not to have got more from the game but admits his side, playing in the competition for the first time in seven years, were not up to the level of the 2019 champions.
“We played a really tough opponent and we put in a huge effort right to the end,” he said.
“It is pretty indicative of the level we have achieved so far. Liverpool are at a high level but we are not quite there yet.
“We were very good after the first 25 minutes, when we found ourselves having a tough time, we went into the lead and were a couple of inches away from going 3-1 up and that might have taken things away from Liverpool.
“It is a shame we got caught out with that set-piece towards the end.”