The Manchester United boss made the claim on Friday as both bosses seek to let their feud fizzle out. Perhaps his Chelsea side still hasn't recovered from the festive period workload and hasn't had sufficient rest time.
The enmity between the two men stretches back to early last season, with Mourinho accusing Conte of humiliating him with the scale of his celebrations as United fell to a 4-0 defeat at Stamford Bridge in October 2016.
But Conte felt the Spaniard was not at fault for his goals drying up, having netted 12 for them in all competitions already this season, and felt the issue ran across the team.
"The first thing I have to find is the right balance".
However, although Conte admits he is a huge admirer of the England worldwide, he says that Chelsea are not considering a move to sign him.
"It was the same".
"This is not a problem with the system". Compared to last season we are conceding less, we are showing great solidity defensively. "We just have to keep working and keep trying to win every game".
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One Chelsea fan who is anxious about the situation in London is former snooker world champion Neil Robertson.
"I think we played with a lot of top players against Arsenal, and then again today against a very good team", Conte told the BBC. "We didn't play well but that's when we need the fans behind us".
"My plan was to play with one team in the FA Cup, and then these two games with nearly the same players".
"Giorgio is a fantastic player but I think he wants to finish his career at Juventus".
The second half picked up where the first half left off, as Chelsea continued to look off the pace in the games.
Even when flanked by Willian and Pedro after the Italian's tactical change, the striker lacked the imposing swagger and confidence to really get engaged with the game. We created chances to score. We played the game against Arsenal on Wednesday night and we didn't have a lot of time to recover. "But at the end I think the result was fair". Once Eden Hazard and Cesc Fabregas were (bizarrely) withdrawn on the hour mark by Antonio Conte, it was clear to see that it was going to be another one of "those days". I saw Eden (Hazard) was very exhausted so he came off.