Pochettino raced onto the pitch at the final whistle after hat-trick hero Cole Palmer scored the latest ever winning goal in a Premier League game after 11 minutes of added time, having equalised a few seconds earlier from the penalty spot.
"It's important in the end to finish in the way that we finished, creating I think the connection (between) fans and players," the Argentine coach told reporters.
"It's a very good thing that happened today and I think should be a turning point for us, creating trust with the fans and in the team," he said.
A few weeks ago, Pochettino - former manager of Chelsea's rivals Tottenham Hotspur - was the subject of crude chanting by some fans during a stalemate at Brentford and on Saturday the boos rang out again after a 2-2 draw at home to 10-man Burnley.
However, asked after Thursday's dramatic last-gasp win about the complaints from some fans that he does not show enough emotion to connect with them, Pochettino said he was focused on doing his job on the touchline.
"I am head coach. If someone wants a clown, they can go and find a clown," he added.
Pochettino paid tribute to the irrepressible Palmer who has now scored 16 league goals, only two fewer than his former Manchester City team mate and top marksman Erling Haaland.
"One of the basic skills is his mentality, his capacity to deal with the pressure," Pochettino said of Palmer. "I think it’s amazing the way he can deal with the pressure."
Manchester United manager Erik ten Hag was left to rue his side's failure to see out a win for the second time in a matter of days, having conceded a very late equaliser to draw 1-1 away to Brentford at the weekend.
"We didn't bring the win over the line. Of course that’s frustrating," he said. "You have to do your job. They know their job and they didn’t make the right decisions."
Ten Hag said he did not know the extent of injuries that forced off two of his defenders - Raphael Varane and substitute Jonny Evans - potentially adding to gaping holes in United's back line before Sunday's visit of league leaders Liverpool.
