Conte complained before the Premier League contest that his players did not have sufficient recovery time following the midweek trip to face Qarabag in the Champions League and might have feared the worst when Liverpool's ex-Chelsea winger Mohamed Salah opened the scoring in the 65th minute with his 15th goal of the season.
But Willian, who scored twice in a 4-0 stroll against the Azerbaijani champions, levelled matters with five minutes to play when his attempted cross looped over Liverpool goalkeeper Simon Mignolet and in.
"I think for the whole game we had a really good performance," Chelsea boss Conte told BT Sport. "In the first half we were very, very solid and always dangerous.
"In the second half I think that we created a lot of chances and conceded the goal in maybe our best moment.
"Then we found the strength for an amazing reaction. I think we deserved to draw and maybe to win."
On Willian's goal, Conte added: "I didn't speak with the player about the goal, if he tried to kick and score in this way, but we deserved to score.
"It was a really good performance, with great spirit despite a long travel and no rest for my players.
"I am very pleased for their commitment and the spirit that they showed in this game."
Manchester City can re-establish an eight-point advantage over their rivals at the summit with victory over Huddersfield Town on Sunday and Chelsea captain Gary Cahill conceded it had been a good day for Pep Guardiola's men.
"I'd say so, if we were in their shoes we'd be delighted with that," he told BT Sport.
"But we have some good games coming up and clearly this is a difficult place to come. It was important we didn't lose so we'll take it and move on."