The Blues’ boss ran down the touchline after Reece James made it 2-1 to his side.
However, Tottenham Hotspur levelled it up at the death courtesy of Harry Kane’s header.
It was a heated afternoon at Stamford Bridge and Tuchel and Conte clashed in the technical area after Pierre-Emile Hojbjerg’s equaliser on 68 minutes and both picked up yellow cards.
They then had another altercation at the end when shaking hands, which resulted in red cards for both managers.
Gallagher, who is now a retired referee, has had his say on the incidents. When asked whether the situation at the end warranted two sending offs, he said:
“I think (yes) in view of what had happened before. Don’t forget they were both on yellow cards as it was. I think it was just inevitable that two red cards were going to come out for the managers.
“It is just not what you want to see at a football match.”
On whether he was surprised that Tuchel avoided a second yellow for his celebration after James’ goal, Gallagher said:
“I was. The feeling from the officials was that it was not inflammatory, it was a celebration, but it was not a wise thing to do. He was lucky but he got punished in the end.”
What next for Chelsea and Spurs?
Both Chelsea and Spurs have four points after the first two matches of the new season.
The Blues are back in action this weekend with a tricky away trip to Leeds United as they look to pick themselves back up.
Conte’s side, on the other hand, return to the Tottenham Hotspur Stadium to face Wolves.