The 23-year-old, who won his first cap for Spain in February, has had an eventful first season in England since arriving from Marseille for £6.5m in August.
However, he has established himself as a regular starter since Rafa Benitez took charge on an interim basis following the departure of Roberto Di Matteo in November.
Azpilicueta told Revista de La Liga: "When I came here Di Matteo was champion of Europe, they'd won the Champions League and FA Cup with a team that was in trouble.
"He took the place of manager and gave me the confidence to play. I didn't play a lot in the first two months with him but in every training he was always trying to improve little things.
"In November with him we didn't get results and here we know you need always to win. This is the pressure and the difficulty.
"We are players of Chelsea, when they change the manager we have to be focused with the new manager to get our objective.
"We were disappointed to lose the World Club Cup, the Capital One Cup, the FA Cup - now we have two targets to get in the top three for the Champions League and to win the Europa League.
"We can be the first team to win two years in a row the Champions League and the Europa League and I think everybody would be proud if we did it."