The Blues somehow overcame John Terry's first-half sending off at the Nou Camp to progress to the Munich finale.
Chelsea came into the match boasting a 1-0 first-leg lead but went behind to goals from Sergio Busquets and Andres Iniesta, either side of Terry's sending off for inexplicably kneeing Alexis Sanchez from behind.
However, Ramires clawed a goal back in first-half stoppage time with a deft chip and, after Lionel Messi missed a penalty and hit the post, Fernando Torres came off the bench to wrap up victory late on.
"It was an incredible game with all the events that happened," Di Matteo said.
"I am very happy and pleased for all the players because they deserved this moment.
"We've had a difficult season and we seem to always get something special out when we need to.
"I think that's part of the DNA of these players.
"Barcelona are the best team in the world. They are amazing.
"They have some of the best players in the world as well in their team.
"The way we played and defended and we just showed a lot of desire to reach the final and go through.
"We had a little bit of luck as well, which you need but I think to win the trophy, you need that."
Chelsea will find out their opponents for the May 19 showpiece tomorrow when Real Madrid and Bayern Munich meet for their semi-final second leg.
"I am just delighted for the players," Di Matteo added. "They put so much effort into this.
"We seem to always to find some reserves from somewhere, playing against the odds.
"We obviously weren't the favourites, even after that first leg.
"We had all the difficulties that you could imagine in any football game tonight, particularly with the way Barcelona play, but we still managed to qualify. It's quite incredible."
While Di Matteo was understandably elated, Chelsea's progression from the semi-finals has come at a huge cost.
Terry, Ramires, Branislav Ivanovic and Raul Meireles are all suspended for the final, while the Blues saw Gary Cahill limp off with a hamstring complaint early in tonight's match.
"For the moment, we'll try and enjoy this night because its quite historic for our club," Di Matteo said.
"Then we will see which players will be available for the final and I'm sure we'll put a strong team together which will make Chelsea Football Club proud.
"On the sending off, we're all human beings. We are put under pressure every three days.
"This was our fourth game in nine days, and you know everybody can make a mistake.
"We work as a group and we're delighted we've gone through."
Barcelona counterpart Pep Guardiola seemed shell-shocked when he made his late appearance at the post-match press conference.
"The first thing that crosses my mind is huge sadness," he said.
"I think we played exceptionally well and we have done everything we could to reach the final.
"Finals are great but we will have to watch this one on TV and I have to congratulate Chelsea because they were great defensively speaking.
"I think we failed because we did everything we could but we couldn't score [another goal] and football is about scoring.
"They scored at key moments but having said that we have worked very hard to get here and there is always this possibility.
"You can win and get the trophy or you can lose and today we lost."