In one of the most remarkable nights in the illustrious competition's history, a Chelsea side reeling from the dismissal of captain John Terry came back from 2-0 down to draw 2-2 and seal a 3-2 aggregate win over the Catalans.
Brazilian midfielder Ramires and striker Fernando Torres scored the goals which secured Chelsea's passage to the Munich final after Sergio Busquets and Andres Iniesta had put Barcelona in the driving seat.
But Chelsea owed everything to a heroic collective effort from a battle-hardened group of players who once again managed to pull victory from the jaws of defeat.
"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; they always seem to dig something special out when they 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."
Di Matteo has presided over a remarkable transformation in Chelsea's fortunes since he took over following the dismissal of Andre Villas-Boas in March.
At that time, Chelsea were on the brink of Champions League elimination following a calamitous 3-1 first leg defeat to Napoli.
However with Di Matteo at the helm Chelsea overturned that deficit with a 4-1 win at home and with Tuesday's win over Barcelona they now stand just 90 minutes away from an improbable Champions League triumph next month.
But Chelsea, who will face either Bayern Munich or Real Madrid in the final, will do so with a squad which has been decimated by suspensions.
Terry, given a deserved red card for an off-the-ball challenge on Alexis Sanchez, is automatically out of the final while Ramires, Branislav Ivanovic and Raul Meireles all picked up yellow cards which will see them suspended.
Di Matteo sympathised with Terry, who will now be deprived of the opportunity to atone for the 2008 Champions League final penalty shoot-out miss in Moscow that prevented the Londoners from lifting the title.
"He's obviously very sad and disappointed that he got sent off tonight and he won't be able to play the final," Di Matteo said.
"On the sending off -- we are all human beings and we are put under pressure. Everyone can make mistakes, but we're just delighted that we've gone through.
"The success tonight is for the players. They deserve everything. They've put so much effort into this. They always seem to find some reserve from somewhere and play against the odds. It's quite incredible."
Di Matteo meanwhile insisted that Chelsea would be able to field a competitive side in the final despite the raft of suspensions.
"For the moment we will try to enjoy this night because it's quite a historical night for our club," he said.
"We will see which players will be available for the final and I'm sure we'll put out a strong side."
With Terry missing the final in Munich, Chelsea stalwart Frank Lampard is now highly likely to don the armband next month.
Lampard was superb once more on Tuesday, delivering the exquisite pass which led to Ramires' crucial goal to haul Chelsea back into the tie on the stroke of half-time while organising the rearguard action that kept Barcelona at bya.
"It's one of the finest moments I've felt in a Chelsea shirt," Lampard said afterwards. "It was backs to the wall. I know we dug in and people want to see beautiful football, but with 10 men for 50-odd minutes or whatever it was, to perform like that was unbelievable.
"That clock wasn't half slow in the second half! You know they're liable at any moment because of the players they've got in their team but there's a determination about us and you get what you deserve.
"We were all in it together and we dug in."