The Blues overcame their latest adversary to progress into the fifth-round of the FA Cup, following a 2-1 victory against Hull City at the KC Stadium on Saturday.
The visitors were off to a perfect start when Belgium forward Michy Batshuayi latched on to a loose ball to put Chelsea ahead in the sixth-minute.
Frank Lampard’s men could not add to their lead in the first half despite their territorial dominance.
Fikayo Tomori increased Chelsea’s advantage midway through the second-half, but the West Londoners were left anxious till the end of the game after Kamil Grosicki pulled one back for the hosts in the 78th minute.
Azpilicueta has identified his team’s shortcomings and insists they need to improve to keep fighting for trophies.
“We have to improve our game if we want to improve as a team and go far. It is not the first game where we don’t manage the game well. We were punished,” the Spain international told BT Sport.
“If we want to play against the best and fight for trophies we need to improve.”
“We are a team and the season is long. We are fighting in three competitions. Our objective is to go as far as possible. It is our job to be in the best shape possible.”
Chelsea have a daunting task at hand when they visit King Power Stadium next week to face third-placed Leicester City in the Premier League.