The Blues lost 2-1 to Manchester City at Wembley on Sunday FA Cup semi-final, and the defeat means that they have now been knocked out of all seven trophies that were available to them at the start of the season.
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A poor record in key games has plagued the club this season, and Azpilicueta has acknowledged that losing so many important games has become a growing concern in the Chelsea camp.
"It's [losing important games] not normal for Chelsea but it's the reality," he told reporters.
"In the first minutes [against Manchester City] we didn't play our game. We were defending; we didn't create chances. We shot once in the first half. It's true we need to play different."
Tiredness appeared a factor in Chelsea's poor first-half showing against the reigning Premier League champions, and Azpilicueta admits fatigue is having an effect on the squad.
"It's [fatigue] the reality," he continued. "We've played 15 games more than Man City and we played three days ago in Moscow. But we're professionals.
"It's normal that we feel a little bit more tired than the other team. This season we've played a lot of games."
Sunday's game was their 59th of the season so far, but the Spaniard insists the squad must call on all their reserves of strength for what will be a crucial end to the season.
"We wanted to win all the trophies at the start of the season, now the only trophy that we can win is the Europa League," he continued.
"It's difficult but now it's the last month and the best games. We need to be focussed and not think about that [tiredness] because it doesn't matter.
"We need to win and it doesn't matter the way we do it."