The Spanish right-back joined from Marseille last summer and after seeing the Blues fail in three other competitions, is looking for a top-three Premier League finish and success in the Europa League.
Azpilicueta admitted it was not ideal to have lost manager Roberto Di Matteo in November but said the playing group managed to overcome that and get the job done under Rafael Benitez.
"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 told Revista de La Liga.
"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."