Conte dropped Azpilicueta to the substitutes' bench for Chelsea's 1-0 home win over Swansea City last week, marking the first time since December 2015 that he had failed to make the Blues' starting XI.
"When you are 30 years old you have at least five more years", said Conte.
"It was a nice run". With my players I suffer.
The draw for the Last 16 will take place next week, with the reigning English champions now able to get Basel, Bayern Munich, Juventus or Real Madrid.
Asked if watching the Swansea game from the sidelines had hurt him, Azpilicueta replied: "Of course!" Especially how I play, the position I play. "We could face big teams as well so now it's time to focus on the Premier League, on the Carabao Cup and FA Cup that we will start in January and when the Champions League is back in February, we will see how we are".
Azpilicueta rarely exhibits signs of fatigue on the pitch, and he would not be drawn on whether he felt that he needed a rest.
Fabregas also added that he is much happier with the role he is playing this season, saying, "Every time I had an opportunity I gave my all, I delivered and from then on we started to create a relationship".
Chelsea failed to top Group C after drawing against Atletico Madrid on Tuesday night. Speaking ahead of Chelsea's heavyweight clash against Atletico Madrid in UEFA Champions League, Fabregas revealed he was anxious last season but made a decision to put his head down and win his place back in the squad.
"If you remember the second part of last season he started to play with regularity". I wasn't playing, not really part of the manager's initial plans and at that point you can do two things - just give up and accept you're not part of the team or the club in the future.
"We are now second, it's OK, so let's think about the Premier League and the Cups".