"A lot of people had written us off and we showed again what kind of character these players have," said Di Matteo.
The Key Moments
12 mins -
Gary Cahill limps off
26 mins -
An injured Gerard Pique departs
- Busquets puts Barcelona ahead
- John Terry is sent off
- Iniesta puts his side two goals up
- Ramires scores for Chelsea
- Lionel Messi misses a penalty
- Fernando Torres scores to secure Chelsea a spot in the final
"[Barca] are a great team with great players. We showed what we're made of."
Di Matteo admitted the game was made harder by Terry's sending-off for kneeing Alexis Sanchez in the 37th minute, but the Italian refused to criticise his captain.
"[Terry] is a fantastic leader," he told Sky Sports. "Anybody can make a mistake in life. I'm not [angry with him]. We're all human beings and make mistakes.
"It's an incredible achievement by this group of players. The belief was always there. When it is the right time we will think about the final."
Leading 1-0 from the first leg, Chelsea's challenge looked to be crumbling after goals from Sergio Busquets and Andres Iniesta either side of Terry's red card swung the tie in Barcelona's favour.
However, Ramires's chip made it 2-2 in the tie - and put the Blues ahead on away goals - before half-time and Barca's Lionel Messi blazed a penalty against the bar early in the second half to preserve the advantage.
Substitute Fernando Torres ensured Chelsea's progress with a goal in injury time.
The story of Chelsea's win
Blues midfielder Frank Lampard - who set up Ramires for his goal - savoured the result as one of the most special of his 11 years with the club.
"It's one of the finest moments I've felt in a Chelsea shirt," he said. "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 to score 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."
Chelsea's red mist
Four of Chelsea's 12 red cards in the Champions League have come in matches against Barcelona. Only four clubs have had more sendings-off in the competition: PSV (13), Galatasaray (15), Internazionale (17) and Juventus (19).
Defender Ashley Cole was equally enthusiastic about Chelsea's rearguard action in the Nou Camp.
"When you lose quality centre-halves like that against a great team, it's going to be hard," said the England international.
"But we all believed. Not many people did but we did as a group of players, and that's what happened.
"It's hard, but we defended well as a team, got a bit lucky, and Petr [Cech] made some good saves.
"Three to four months ago no-one thought we had a chance. We lost a few games in the Premier League but we always believed and knew we were good enough to be here.
Capital gains from Chelsea win
Chelsea can become the first London club to win the European Cup. Only five European capitals have produced a winner in Europe's premier club competition - Madrid (9), Amsterdam (4), Lisbon (2), Bucharest (1) and Belgrade (1).
"You can't beat that desire and fight that you saw out there today."
The only sour note of the night for Chelsea is that suspensions mean they will be without Terry, Ramires, Branislav Ivanovic and Raul Meireles for the final in Munich on 19 May, where they will face either Real Madrid - managed by former Blues boss Jose Mourinho - or Bayern Munich, on their home ground.
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