However, the west Londoners were well worth the win, which sees them go seven points clear of Tottenham, who face a tricky trip to Crystal Palace on Wednesday.
"We passed a big step, a big psychological step after the defeat against United", Conte revealed.
Conte was happy with the display, a second 4-2 win in four days after Saturday's FA Cup semi-final triumph over Tottenham.
But the Frenchman rued the concession of goals at crucial periods in the game. "I think for us it was important this win". I was pleased for his performance.
"I think we have some players who can be more than a captain in this team", Hazard told Sky Sports.
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"It's normal we have to push to try to keep this position until the end".
Conte added that speculation about Diego Costa's future was being caused by troublemakers after the striker, linked with a summer move to China, scored for the first time in five league matches. "The goal is their life".
"It's always good to play before - Tottenham play tomorrow so we've put pressure on them". He always worked for the team.
"The first target for every great champion is to play for the team and to put your talent into the team", he said.
Hazard scored Chelsea's first following a Fabregas through-ball and Costa lay-off.
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Chelsea were third in Premier League spending last summer but will point to their significantly smaller net spend, given they received big fees for players including £60m for Oscar in the last 12 months.
It will not be an easy game for Mauricio Pochettino's men as Palace have beaten Chelsea, Arsenal and Liverpool in recent weeks. "For me, it will be a great loss next season to lose a player like this".
"John, for us, is a really important player", Conte added "He is doing a great job this season. It's important to look at ourselves and not the other". "I hope they have trouble. In this part of the season, it's not easy".
"He scored two very important but also lovely goals, with good combination and technique between him and his teammates".
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European Parliament Brexit coordinator Guy Verhofstadt said winning extra seats won't necessarily strengthen her position against the EU.