Holding a 5-2 lead from the first leg, Liverpool were cruising after going 2-1 up in the return in Rome.
But Roma equalised after the interval and scored twice in the final moments of a dramatic tie which set a Champions League semi-final goal record.
Reds captain Henderson conceded Liverpool had made it more difficult than necessary as Jurgen Klopp’s side set up a final showdown with holders Real Madrid on May 26.
“We never do it the easy way unfortunately. We could have done better in this game but we’ve made it through to the final,” Henderson told BT Sport.
“Overall we handled the situation well apart from the last 10 minutes. We need to stop that but I’m delighted we’re in the final.
“We knew it was important to score and get one early on. It was an amazing effort.
“We have another important game on the weekend against Chelsea and then we have Real Madrid in the final. We will go there with confidence.”