Leading 5-2 after the first leg of the semifinal, goals from Sadio Mane and Georginio Wijnaldum should have put the tie to bed but the Italians hit back on both occasions, through Edin Dzeko and a James Milner own goal.
Liverpool weathered an early Roma storm in the second half and were left thanking the referee who missed two clear penalties for the home side.
Two late Radja Nainggolan goals, one a strike from distance and the other a stoppage-time penalty, ensured the closing stages remained interesting but they proved nothing more than consolations in what was the highest scoring semifinal in the competition's history.
"We are all inclusive, sometimes I like it, sometimes I don't need it and after the game I'm fine with it," Liverpool manager Klopp told BT Sport.iPhone transfer software
"We should start winning (finals), I know that. I said it before the semifinal, everybody will remind me from now on that I lost the last five finals. It was a little bit more exciting than I would have wanted, but now it's over I'm fine.
"It's a final, the boys deserve it. The campaign, the character they've showed, the mentality they've showed, the football they've showed, it's just crazy. 7-6 on aggregate -- it's unbelievable."
Liverpool fans celebrate reaching a first Champions League final in 11 years.
Roma needed to make history
Roma, knowing only another historic night at the Stadio Olimpico would see them into the final -- they became the first team to come back from a three-goal deficit in the quarterfinals with a dramatic win over Barcelona -- started the match at blistering pace.
Inside the opening 30 seconds, Virgil van Dijk headed away an awkward cross by Stephan El Shaarawy as Edin Dzeko lurked menacingly behind him.
Liverpool's Dutch center back then did well to intercept a through ball aimed toward Dzeko, while another run in behind the defence by Dzeko had goalkeeper Loris Karius scrambling across his goal. Alessandro Florenzi also went close with a long-range shot.
It was breathless but, unlike the quarterfinal second leg against Manchester City, Liverpool weathered the storm comfortably and, against the run of play, took the lead.
Radja Nainggolan under hit his pass back to Federico Fazio and Roberto Firmino pounced on the loose ball before threading a pass into Mane, who finished under the onrushing Alisson.
The only noise which could now be heard inside the Olimpico was the Liverpool fans repeatedly chanting 'allez, allez, allez.'
However, in the blink of an eye, Roma were gifted the smallest of lifelines.
Another ball into the box was seemingly dealt with by Dejan Lovren, but his clearance smashed into the side of midfielder Milner's head and ricocheted past Karius into the Liverpool goal.
Once again, the Olimpico burst to life; flags were waved and 'allez, allez, allez' was soon replaced by 'Roma, Roma, Roma'.
But their optimism lasted all of 10 minutes. Roma's defense, which had been generous to Liverpool over the two legs, again failed to deal with a cross and Wijnaldum nodded the ball past Alisson to give the visitors a commanding aggregate lead.
Roma's Italian coach Eusebio Di Francesco was furious after his captain's costly error.
Needing four goals to even take the tie to extra time, Roma to their credit continued to press forward in the hope of finding the goal that could prove to be the catalyst for another memorable comeback.
El Shaarawy, by far Roma's most dangerous player, had a shot which deflected off Milner and hit the post, before having an appeal for a penalty turned down.
Another shout for a penalty in the second half, as Dzeko was brought down by Karius, had Liverpool hearts in mouths, but they were saved by the linesman flagging for offside.
Replays showed the decision was a wrong one, but Roma continued to press forward and were soon rewarded with another goal.
Trent Alexander-Arnold was unable to intercept Daniele De Rossi's through ball and El Shaarawy cut inside and fired a shot towards goal. Karius was only able to parry the ball into Dzeko's path and the Bosnian striker made no mistake, firing his eighth Champions League goal of the season into the top corner.
To say Roma now believed they could progress would be an overstatement, but they had at least given their fans a glimmer of hope.
It felt like an important period in the game; wave after wave of Roma shirts descended on Karius' box and the keeper made an important save from substitute Cengiz Ünder on the hour mark.
The hosts should have been awarded a penalty, which arguably would have turned the tie on its head, but the referee inexplicably missed a clear handball by Alexander-Arnold as the defender blocked El Shaarawy's goal-bound strike.
Roma's players tired in the closing stages and rarely looked like threatening until, out of seemingly nowhere, Nainggolan scored two consolation strikes which again brought a slumbering Stadio Olimpico to life.
But it was too little, too late and it was Liverpool's 5,000 traveling fans who