The Blues appeared to be heading for a home defeat at Stamford Bridge, with Raul Jimenez scoring the game's only goal heading into stoppage time.
But Hazard came to his side's rescue in the 92nd minute, firing home from the top of the box to give Chelsea a share of the spoils.
Despite Hazard's late heroics, Sarri still appeared to be frustrated by a lack of movement from the Belgian and the rest of his team-mates.
Sarri said he believed that his players were hindering the effectiveness of Jorginho, who looks to control play for the Blues from the middle of the pitch.
“Jorginho, if the other players do not move without the ball, is in trouble, because he is really very able to play with one touch," Sari said.
“Of course if you want to play with one touch you need movements with the other players.
“I know him very well. He can go in trouble if all the rest of the team is not moving.
“We needed to move faster and needed more movement without the ball.
“Today we played with five touches and if there is no space it is very difficult to score if you play with five or six touches.
“We need to improve in this kind of situation. We can’t keep taking five or six touches.
“Hazard is a great player, he can solve this situation, but during the match was like the other players. He needs more movement without the ball.”
Though he was frustrated with his side's static play, Sarri still felt Chelsea did enough to win on the afternoon.
“We made a lot of mistakes but we deserved to win," Sarri said.
“We were unlucky because we conceded a goal in the first situation inside our box – the first and the last in all the 90 minutes.
“We were unlucky on that, but on the other hand we need to improve in attack against teams who defend with 11 players. We must move the ball faster.”
Chelsea are back in action on Thursday when they face Dynamo Kyiv in the second leg of their Europa League last-16 tie.