The Spanish full-back has been part of a Chelsea defence that has managed just six clean sheets in their past 20 games - and two of those were against lower league opposition in the FA Cup.
But the Blues still have a good chance of success in two cup competitions this season - the FA Cup and the Europa League.
And Azpilicueta believes Chelsea's priority should be to sort out their defence before they begin thinking about winning either competition.
He said: "It's true that it is one mistake we are making many times and we need to stop it. The easiest way to stop the counter attack is outside the box and in this area we need to improve."
Chelsea conceded two early goals against Manchester United in the FA Cup quarter-final on Sunday, before eventually fighting back to secure a 2-2 draw and a replay at Stamford Bridge.
And their poor defence was caught out against Steaua Bucharest in the first-leg of the last-16 Europa League tie last week.
Despite their defensive frailties, Chelsea will feel they have a good shot at progression in both competitions. Their FA Cup replay date is yet to be determined but they can take a huge step towards the Europa League final on Thursday by overturning their first-leg deficit.
The report claims that should the Blues progress to the final of both tournaments, they could expect to play 19 games in less than two months.
And Azpilicueta concedes it could be a tough ask, after a marathon campaign for club and country. Still, he's ready to help the team.
"It's true that it is a long season," said the Chelsea right-back. "I started on July 1 with the national team at the Olympics and then started a very difficult season with Chelsea, playing a lot of competitions. But we have two months in front of us to win trophies."