Liverpool suffered defeat for the first time in 2022, but still progressed to the last eight of the Champions League on aggregate.
Lautaro Martinez's second half stunner ensured Inter were the victors on the night, but the Reds move on 2-1 over the two legs.
The Italian champions arguably started a little better, pressing Liverpool's midfield trio of Curtis Jones, Thiago and Fabinho.
A bitty first half was paused due to a medical emergency in the crowd, with responders quickly addressing the situation in the Kop.
After resuming Joel Matip and Virgil van Dijk both came close to opening the scoring, with the former hitting the crossbar from a fizzing Trent Alexander-Arnold free kick.
Hakan Calhanoglu had Inter's best chance of the opening 45 when his stinging set-piece was pawed away by Alisson in the Liverpool goal.
Five minutes into the second half, Mohamed Salah looked destined to open the scoring, but after following up on a Diogo Jota effort, he could only hit the post with the goal gaping.
Martinez spurned a wonderful chance to open the scoring, but made up for it a couple of minutes later as he arrowed a shot into Allison's top corner to give Inter the lead on the night, halving their arrears in the tie.
But the wind was instantly taken out of the visitors' sails, when Alexis Sanchez was sent off after picking up his second yellow card for a clumsy tackle on Fabinho.
With the man in advantage and the game somewhat back under their control, Salah hit the post for the second time of the evening with just over ten minutes remaining.
Liverpool had further chances to put the tie beyond Inter, but held on to qualify for the next round, despite losing for the first time in 15 matches.
Here are the main talking points from Anfield:
A year is a lifetime…
Rewind to March 7, 2021, and Liverpool lined up with a back four including Neco Williams, Nat Phillips, Rhys Williams and Andy Robertson.
A year on, Joe Gomez was on the bench and Ibrahima Konate was left out of the squad as a precaution.
It marks a dramatic change in the strength in depth Klopp now has at his disposal, with the German admitting the ability to rotate players was an issue he'd never had before.
"It (a fully fit squad) is a good situation to have, no doubt about that, but I don't know how often I have to say it is much more important how we play than who is playing," he said ahead of the first leg.
"It helps that we have solutions for different problems, options for different situations.
"It means I cannot always play the same line-up just because we won the last game. It is something we have to learn together and that's what we do.
"We never had it before. It is pretty exciting."
Sanchez's woes continue
Alexis Sanchez returned to Anfield looking to reverse a wretched run of form at Anfield, in his six seasons in English football, the Chilean failed to win a single game, or score a solitary goal.
His time with Manchester United meant it was expected he would get a special reception from the Kop, but that only came after a nasty challenge on Thiago reminded Liverpool fans he was on the pitch.
He probably should have seen red for that, but just minutes after his strike partner Martinez had put Inter in front, he lunged into another tackle, picking up a deserved second yellow - an incident which ultimately ended his side's hopes of an unlikely turnaround.
Sanchez worked hard during his 63-minute cameo, but he still looks miles off the player that terrorised Premier League defences with Arsenal all those years ago.
Light metal football
Klopp is never shy in coming forward about fixture congestion and did so again this week, labelling the current pile-up as "horrible".
But such are the drawbacks of trying to achieve something no English team has ever done - winning all four major trophies on offer.
The Reds boss insisted his side would be on the front foot, but with another three matches next week, it made sense to ease off a fraction with the two-goal lead they earned from the first leg.
Inter are no slouches and had they come into this second leg level pegging they would have needed to be in top gear to be sure of their progression.
Their advantage allowed Liverpool to manage the game and play at a level below their 'heavy metal' best. It could prove valuable come the real business end of the campaign.
Trent sends a message to Southgate
With Gareth Southgate set to name his England squad in the next week or so, Alexander-Arnold proved that any myths over his lack of defensive abilities have been greatly exaggerated.
His club manager, Klopp spoke in frustrating tones about the narrative which seems to surround the right-back.
"Absolutely, I don't understand that, that's true, but I don't think I will change that with whatever I will say," he said earlier this week.
Liverpool may have shipped a goal against Inter, but Alexander-Arnold put in an impressive display at both ends of the pitch.
On two occasions in the first half, it was his positioning which nullified attacks, while his delivery in the other box was unsurprisingly, fantastic.
The battle between him and Reece James over that berth is set to go all the way to Qatar, but on this form it's difficult to not include the Liverpool man.
Another step closer to history
As Liverpool clear each hurdle it is worth taking a step back and assessing just what they are trying to achieve.
Carabao Cup in the bag, in the last eight of the Champions League and the FA Cup and the Premier League title race set to go down to the wire, it promises to be a remarkable end to the campaign.
Inter Milan came to Anfield as the Italian champions and had they not come up against Liverpool, would have likely continued their own European adventure.
The Reds weren't at their best, but it's another step closer to sporting history and although the odds are still up against them, it would take a wise person to bet against them.