Man-of-the-match Hazard put Chelsea ahead from the penalty spot and, following James Collins' equaliser, Diego Costa struck a last-gasp winner to seal a 2-1 victory on Monday.
Conte celebrated wildly with the Chelsea supporters on the touchline and was full of praise for his players' performance in his first game at the helm.
"The team played a good game with great intensity and good spirit. There was great intensity and positioning. It was also very physical. I am delighted with the performance," Conte said.
"It's important to find the right spirit and intensity, we know that we can improve and we must improve a lot, but I am pleased for the team. Eden played a good game. He has great ability and is very important in this team," he added.
"I am very pleased with his performance but I know, and he knows, that he can improve a lot. The victory was deserved for me. Now we have to prepare for the next game."
The former Italy head coach revealed he had thoroughly enjoyed his first experience of football in England, despite being forced to wait until the 89th minute to seal victory.
"I only knew the league through television and having played against English teams in the Champions League and Europa League, but it is very difficult. The atmosphere was fantastic and I want to say thank you to the fans because they followed the players at the end," he said.
"It was fantastic and emotional for me to see the Italian flag in the crowd," Conte signed off.
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