The young full-back netted his first competitive goal for the Blues as they earned a 2-0 victory against their London rivals in the fourth round.
Mata believes that Azpilicueta deserved his place on the scoresheet due to his hard work for the team.
"I am so happy for Cesar," the Spaniard told the club's official website. "He trains more than anyone and he fully deserves it, the goal and the celebration after.
"He is always ready to play, like everyone in our squad. Yesterday was his day."
Chelsea return to action on Saturday when they travel to Newcastle United in the Premier League.