Chelsea's Pochettino criticises social media abuse of Gallagher
Chelsea said in a statement the "defamatory comments" made towards Gallagher were "completely unacceptable" and that the video had been taken out of context.
The incident took place before kick-off in Chelsea's match against Burnley at Stamford Bridge, with the 24-year-old seemingly unaware that one of the mascots had held up his hand.
Pochettino rejected any suggestion that Gallagher acted intentionally as he hit back at the online reaction.
"It has upset me so much," he said. "No one wants to do this with this intention. When you are focusing on playing and starting the game, that sometimes can happen."
The Blues boss added: "People always try to find things to create a mess. I know Conor. Come on -- there's never that intention.
"Conor is a great kid and always is caring about everything. I hate how people feel free to abuse on social media."
Pochettino has previously spoken out about the impact of online abuse towards players and said action was needed to deal with the issue.
"Today, abuse of people is so easy," the Argentine said. "Whenever this type of thing happens, we (must not) give too much attention to the type of people that want to create it, to insult and abuse other people. Please stop.
"How is it possible to believe that Conor's intention is to ignore a mascot? Come on. It makes me very sad.
"Our responsibility is to try to ignore this type of thing. The people that try to create it never help our lives. They don't deserve attention."
Pochettino also highlighted the case of Barcelona defender Inigo Martinez, who was filmed tis week getting out of his car to remonstrate with a fan who had criticised him verbally.
The Chelsea manager suggested the player had been provoked so his reaction could be filmed and posted online.
"It is society that consumes (this material)," he said. "All that people are interested in are bad things.
"We are a bit responsible also. We opened the door, all the documentaries. People want to see when we are fighting but never things that are good, happy things. They want to find the wrong things. That is the society that we are all involved in."