Liverpool boss Jurgen Klopp claimed referee Michael Oliver refused to let him make a substitution prior to Chelsea's crucial equaliser at Anfield.
Substitute Willian secured a 1-1 draw for the Premier League champions on Saturday when he lobbed Simon Mignolet from a tight angle in the 85th minute.
Liverpool had seemed on course for victory after taking the lead through former Chelsea forward Mohamed Salah after 65 minutes.
Klopp claimed he wanted to introduce Adam Lallana and change his team's shape to protect the lead but said he was made to wait by Oliver.
The German told BT Sport: "I was angry because we wanted to change the system but the ref didn't give us the opportunity. I don't know what he thought in this moment, he told me something about taking too long, I don't understand it.
"How can we take too long? We didn't want to time waste, we wanted to change the system and that's why I was angry."
He added in his post-match press conference: "In my mind Ragnar Klavan would have been exactly in the position where Willian crossed the ball. Maybe we would have blocked the cross. So, it doesn't feel too well when we couldn't change the system."
Klopp also thought Willian's late effort was unintentional.
He said: "Everything was good until Willian crossed the ball. Most parts of the game were good but it doesn't feel it.
"But that is how it is. We will be better. The world is a strange and a crazy place at the moment so I can easily live with a point against Chelsea.
"It was a good game, an intense game and a very difficult game against a strong Chelsea team."
Klopp played down what appeared a disagreement with Sadio Mane, who came on as a late substitute.
"It is not a big thing," said Klopp, insisting the matter was about positioning. "We could have done it in the dressing room. Everything was sorted immediately."
Conte was pleased with his side's efforts, coming after a midweek trip to Azerbaijan in the Champions League.
The Italian said: "I think we must be pleased. Both teams played with a great intensity from the start to the end.
"It was very difficult to play this game after a long travel and no rest for my players, and also because when you play at Anfield it is not simple.
"In our best moment we conceded the goal and were unlucky. But at the same time I was very happy to see a great reaction from my players, with the way they fought and didn't accept a bad result at Liverpool.
"We tried also to win the game and I think we must be pleased despite the draw. I think it was a fair result but in the end we deserved a little more."
Conte gave a diplomatic answer when asked whether Willian's strike was intentional or not.
He said: "I must be honest - I didn't speak with the players. It's not important! It is only important to score."