The Blues' defence of the Champions League title won last May ended limply before Christmas, but now their attention turns to the Europa League last-32 in Prague on Thursday night.
"We want to play every few days because it means we are still in competitions," Azpilicueta, who impressed in Saturday's 4-1 Barclays Premier League defeat of Wigan, said on chelseafc.com. "It is very important for the team to keep going in the Europa League and the FA Cup."
He went on: "It is true the Europa League is not the same as the Champions League because that is the top but the Europa League is a big competition, an important competition, and now we have the chance to win it.
"Never in the history of Chelsea have we won this cup and we are going to try to do it."
European Cup-winning manager Roberto Di Matteo was replaced by interim boss Rafael Benitez when Chelsea failed to advance from the Champions League group stages.
Chelsea have struggled for positive results in recent weeks, including drawing at npower League One Brentford, resulting in this week's replay.
Azpilicueta, though, is confident Benitez's methods are working.
"The first months I was here we had Roberto [Di Matteo] with us and now Rafa came here and we are working very hard with him," added Azpilicueta, who won his first cap for Spain last week. "We are trying to do the things that he asks and I think that we are playing well and doing the right things.
"When we have lost we have done a good game but when you make mistakes you pay. When you don't win it is difficult but hopefully we now recover the smile that is important for the team and for the future."
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- Europa League
- Roberto Di Matteo