Hazard scored a sublime solo effort at Anfield in the EFL Cup in midweek and netted his seventh goal of the season to nudge Chelsea ahead at Stamford Bridge.
But Sarri - who also acknowledged that the Blues must not rely too much on Hazard - was pleased with the playmaker's all-round effort, having this week questioned his intensity in training.
"I'm really very happy with the defensive performance of Hazard today, especially in the second half," Sarri told a post-match news conference.
"I think at the end of the season we can have four, five players over 10 goals. And so it's not only Hazard.
"Of course, Hazard is the first, but I think Pedro, Willian, [Alvaro] Morata, will be able to score more than 10 goals in a season."
Liverpool cancelled out Hazard's effort through Daniel Sturridge's 89th-minute stunner, extending their unbeaten start to the league season to seven matches.
Chelsea are also still to taste defeat under Sarri, and the former Napoli boss says the Blues can be buoyed by their display.
"I am disappointed because they scored in the last minutes," Sarri added.
"But at the end I am really very happy - first of all with the performance and I think also a draw is the right result. The match was wonderful.
"I think [Manchester] City and Liverpool are a step ahead of us. It's very difficult. I think we can fight for the Champions League places.
"Here it's very difficult to arrive in the first four. There are six, seven top-level teams, top in Europe, not only in England.
"It's not easy to get in the Champions League. We have to try of course. We have to try to stay very close on the table with the top-level teams. And we have to try to improve."