Barnes caught Matic high on the shin during the 1-1 draw at Stamford Bridge, provoking an angry reaction from the Serbian.
Matic chased after Barnes and pushed him to the ground, earning himself a red card while Barnes received no punishment.
Jose Mourinho appeared on Sky Sports' Goals on Sunday programme the following day to condemn Barnes' challenge, before Burnley boss Sean Dyche defended his striker.
"To be honest I was happy when I saw the video after the game - as it was bad. I am happy that I can still play," Matic is quoted as saying by the Daily Mirror.
"My reaction was not good but this reaction was because I thought I broke a leg. I am a happy man because I can walk.
"I don't like to say that I was right to react like I did. I was not right.
"But this was a moment when you cannot control your emotions. I saw a replay one time only - that was enough."
