The Italian boss was replaced with Rafael Benitez by owner Roman Abramovich after the side's league form slipped and a 3-0 defeat to Juventus left them unlikely to reach the knockout stages of the Champions League.
But despite the protestations over the dismissal of a man who won a European and FA Cup double just months before, the keeper says the club must move on - and even gave the players a speech on pulling together.
"It was sad to see [Di Matteo] go early like that, but that's football life, unfortunately," he told the Daily Mail.
"He will always be a huge part of the history of this club with all he has achieved as a player and manager."
After his side's surprise defeat to West Brom last weekend, Cech said he made a dressing-room talk on the importance of the task ahead of them: "It was a speech I had to make to the team about what we are and what we want to be and that we have to improve if we are to fulfil our expectations.
"We were all in the same boat - manager, coaching staff and all players.
"We've ended up in this situation and we are all responsible for that, so we need to put it right now. Unfortunately, the manager is always the one who gets under pressure the most."
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And despite the Stamford Bridge club's stuttering recent form, the No.1 keeper feels the signings are helping to alter the club's playing style for the better.
He continued: "You can see the change of the generation is happening slowly but surely.
'We have a lot of new players and players that haven't been here for a long time. So it feels like a new Chelsea and obviously the players are really different players and have brought a different style; their way of playing football is completely different.
"If you have Juan [Mata] and Eden [Hazard] on one side and they're standing next to [Ryan] Shawcross and [Robert] Huth, there's no point kicking the ball."
And rather than the change of tactics, Cech thinks the side's stuttering form is simply down to poor defending: "We had a very good start to the season so I don't think it all happened too quickly. You need to defend as a team to defend well."