Costa completed an emotional return to Atleti — whom he joined Chelsea from in 2014 — last week following a controversial close season, but is not eligible to play until January.
The striker, having powered his side to the Premier League title last season, failed to secure a move during the transfer window despite being deemed surplus to requirements at Stamford Bridge.
However, he is now back in the Spanish capital — and Azpilicueta wished him well, all the while admitting he is pleased not to be taking him on at the Wanda Metropolitano.
He said: "I was lucky enough to have played with Diego Costa with Chelsea and Spain, where I hope to meet him again very soon.
"He's now decided to change, so best of luck to him. He was important to Chelsea while he was there, but now he's moved on.
"We have to deal without him. Obviously, not to play tomorrow with Diego in Atletico is better for us.
"As I said before, I played with him for two years, we're Spanish team-mates, and he's a top striker. Not to play against him is a little advantage for us."
Conte says he has no problem with Diego Costa and wishes him the best for the future.— Chelsea FC (@ChelseaFC) September 26, 2017
Any heartache among Chelsea fans at Costa's loss has been offset by Alvaro Morata's flying start to life in England.
The striker has netted six league goals already for the London club — and Azpilicueta is understandably delighted to see his quick acclimatisation.
He added: "Well, I think he has adapted really well to our team, to the way we play since he came. His desire to perform, to be a big part of the team, has been huge.
"I know the work he has been doing. He got the rewards that every striker wants: he's scored six goals.
"I've tried to help him since he came to London, on and off the pitch, and I'm happy for him because the work he's been doing... he's scoring goals, and that's the main thing for him."