Olivier Giroud and winger Pedro also got on the scoresheet to help make the Belgium international's potential goodbye appearance a memorable occasion.
"It's a big loss for us, as a player and as a person," Azpilicueta told beIN Sports .
"We came here together seven years ago, we have won six trophies, it's been amazing on and off the pitch for me.
"I can only wish him the best because he's a very good friend of mine.
"The desire he's shown on the pitch for the club, his behaviour as the star man, I think everybody in the club loves him.
"He's not selfish - a lot of times I heard rumours about him leaving. In other situations maybe other players could push but he didn't do it.
"I can only say all the best and we're going to miss him."
Maurizio Sarri's future at Stamford Bridge is also uncertain amid links to the vacant Juventus post.
The Italian guided Chelsea to a major trophy and Champions League qualification at the first attempt but, when asked whether his head coach should stay, Azpilicueta noted the decision is out of his hands.
"It's not my choice. Obviously Maurizio is the manager," the Spanish full-back said.
"We started the season quite late. In February, March we were in difficulty, we were sixth in the Premier League and everybody thought we were out of the Champions League.
"We came back, we finished third... lifted the Europa League [and] lost on penalties in the Carabao Cup [final]. I think if you look at the whole season it has been very great."