The Blues suffered another disappointing blow to their hopes of finishing in the top four on Sunday afternoon when they were pegged back and held to a 1-1 draw by West Ham United in the Premier League at Stamford Bridge on Sunday.
That result left Antonio Conte’s side in fifth place in the table and 10 points behind fourth-placed Tottenham Hotspur with just six games left to play.
It means that the Blues are likely to have to settle for a place in the Europa League next season as they look set to miss out on a place in the top four for the second time in three seasons.
Chelsea FC are still in with a chance of ending the season with a trophy and they will take on Southampton in the FA Cup semi-finals at Wembley later this month.
However, Chelsea FC defender Azpilicueta has warned the Blues that winning the FA Cup would not mask that fact that it has been a disappointing campaign for the west London side.
Speaking to BBC Sport, Azpilicueta said: “The FA Cup is a massive trophy with a lot of history but it’s not enough for us.
“We will try to win it but the cup will not save our season.”
Chelsea FC will travel to Southampton in the Premier League on Saturday lunchtime.
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