The defending Premier League champions lost to Tottenham Hotspur at Stamford Bridge for the first time since 1990 on Sunday evening.
Christian Eriksen cancelled out Alvaro Morata’s headed opener before England international Dele Alli scored twice in the second half.
Spurs moved eight points clear of Chelsea FC in the Premier League table to give them a significant cushion in fourth place.
The Blues still have to play third-placed Liverpool FC in their penultimate Premier League game of the 2017-18 season.
The challenge for the west London side will be to get within striking distance of the Reds ahead of their top-flight clash at Stamford Bridge.
Azpilicueta is adamant that Chelsea FC aren’t giving up on the possibility of a top-four finish in the Premier League this term.
“It [the top four] looks further away than it did before the game but there are still points to play for,” Azpilicueta told Chelsea FC’s website.
“With every game you play you are closer to the end and we have to make sure we try to get there.
“It’s a hard kick for us because our target was to get closer to them and after the game we are even further away, but it’s a massive target for us so we have to make sure we fight until the end to try to get that spot.”
Chelsea FC won the Premier League title with two games to spare last season after Antonio Conte’s men finished seven points ahead of Spurs.
The Blues will take on Southampton in the FA Cup final at Wembley this month as the Italian head coach looks to win the competition for the first time.
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