The Blues were beaten 3-2 by the visitors at Stamford Bridge after seeing Branislav Ivanovic and Fernando Torres sent off in the second half.
Di Matteo was unhappy with Torres' dismissal after Clattenburg adjudged him to have dived and handed the striker a second yellow card, despite Jonny Evans appearing to make contact.
The Chelsea boss also insists Javier Hernandez's winner for the Red Devils was from an offside position.
He told Sky Sports: "The key decisions from the referee today probably influenced the result.
"He sent off Fernando Torres and the third goal is offside and that clearly has decided the game for our opposition tonight.
"He's (Torres) put the ball between his legs and he's through and he gets kicked on his shin and he goes down. It's as simple as that. It's a free-kick for us. It might even be a sending-off for Evans because he's through on goal.
"I was shocked. I thought it was going to be a free-kick for us, and a foul for us, not against us.
He added of Hernandez's goal: "I watched it again and the replay shows when Rafael shoots he's in an offside position."
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
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