The Argentine said it was normal for Chelsea fans to be sceptical given his affiliation with rivals Tottenham Hotspur but it was a matter of time for that trust to build.
Pochettino guided Spurs to the 2019 Champions League final and turned them into Premier League title contenders as they finished in the top four for four straight seasons before he was fired in 2019. Chelsea appointed him in May last year.
"You need to convince," he told reporters after Thursday's dramatic 4-3 home win against Manchester United. "You arrive at Chelsea in a project that is different to the last 20 years.
"I played with my reputation to come here also, in a project that is to build a team with young talented players with the possibility of the potential to become top players.
"For us, we knew that was a massive challenge. A challenge of building a team, winning games, being competitive and to take the risk with the fans. But I'm not going to be a populist.
"I said from the beginning that I want to build a genuine relationship - not to kiss the badge or to do stupid things on the touchline to win the benefit of the fans."
Against United, 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 with a penalty.
Chelsea are in 10th place with nine games to go and next visit bottom side Sheffield United on Sunday.
"What I want is to provide to the team the tools to win games, believe in ourselves and build a very good relationship," Pochettino added.
"I am not here to be a populist or a hypocrite and say 'Oh I love the fans' because I know, always it is about time to build this relationship."
Pochettino said Chelsea need to focus on being consistent after their latest result.
"Three points in Sheffield. If we want to be close again, it's about winning... If we win all the games, for sure we will be in Europe. But it is about Sheffield now," he added.
England left back Ben Chilwell is not back in training, having missed Chelsea's 2-2 home draw against lowly 10-man Burnley on Saturday with a leg injury after returning from international duty. He missed the United game through illness.
