He said: "He was lively, caused a few problems, had a couple of opportunities, we saw glimpses of his quality, and he will be a big success for us.
Hazard became the most expensive Premier League signing of the summer so far when he joined the Blues from Lille in a £32million deal in June.
The Belgium international comes with a huge reputation having been named Ligue 1 Player of the Year in each of the past two seasons.
With supporters excited at the prospect of Hazard helping the Stamford Bridge outfit launch a serious title challenge, the 21-year-old playmaker has moved to downplay expectations.
"I am going to play bad games," Hazard told The Sun.
But Hazard takes a phlegmatic approach to any potential difficulties that lie ahead.
He added: "My transfer fee does not put pressure on me. I am 'Zen' - very calm - about it."
Di Matteo also praised Torres for his display but emphasised that the burden of scoring goals should not fall solely on the Spanish strikers' shoulders.
"Fernando (Torres) was also dangerous in what was his first 90 minutes since coming back into training under three weeks ago.
"But we have to share the responsibilities for goals between the team - Hazard, Torres, Ramires, (Juan) Mata, (Daniel) Sturridge, (Frank) Lampard can all score goals."
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Di Matteo claimed the red card issued by referee Kevin Friend was the key moment in the game.
He said: "It changed the game in favour of Manchester City. We competed very well and at that point were in the lead.
"It was difficult in the second half against 10 men.
"The challenge had no intent to hurt the opposition. It was a sliding tackle and he got the ball as well.
"Sometimes a red card is given in those circumstances, sometimes it is not. But there was no intention to harm the opponent."