"Well, I would be lying if I say that I wasn't anxious", said Fabregas, speaking ahead of Tuesday's Champions League Group C clash with Atletico Madrid.
'The objective has been reached, to qualify, but we won't relax, we want to be first in the group, ' said Fabregas.
Conte believes Fabregas has plenty of years remaining at the top.
Fabregas broke into the first-team fold in the latter stages of the season, however, and has been used far more often so far this time around with 12 starts to his name already.
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"Last season the boss might not have trusted me to play in a 3-4-3 but he does now". "They let me go to get Cesc in", Lampard said on BT Sport this weekend.
Chelsea are preparing for tonight's (TUE) game against Atletico Madrid in the Champions League, the one major competition which has eluded Fabregas in a long and glittering career.
"Physically... I wouldn't say better than ever, but in the last few years I feel the fitness". Especially how I play, the position I play. I tried to make the best decision.
Atletico need to win to have any chance to advance, but are reliant on Qarabag avoiding defeat at Roma to reach the draw on December 11.
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Conte applauded the "commitment" and "behaviour" of Fabregas and agreed the midfielder has the "desire" and "will" to continue into his mid-30s at the top level, despite Chelsea's strict policy of only one-year extensions for all players over 30 years old. "For this reason he is very strong".
Asked if that would provide additional satisfaction, given the saga surrounding Diego Costa which saw the striker return after three years at Stamford Bridge, Conte was evasive.
Fabregas, who was a member of the Spain side that won successive European Championships in 2008 and 2012, as well as the 2010 World Cup, said he could have just given up when Conte didn't initially select him last season.
"If the whole team after (Tuesday's) game has to play Europa League, it can happen".
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