Son has been a focal point during Tottenham's pre-season tour of Asia and Pochettino said the reception of the South Korea international came as no surprise.
The 27-year-old is preparing for his fifth full season as a Spurs player and he has scored 42 goals in 130 Premier League appearances since his arrival from Bayer Leverkusen in August 2015.
Son featured in Tottenham's 3-2 International Champions Cup victory over Juventus in Singapore on Sunday and will be involved again when Pochettino's men face United in Shanghai on Thursday.
Asked whether he was taken aback by the adoration on display for Son, Pochettino told reporters: "No, not surprised. We can appreciate and see how the people love Sonny here in Asia.
"Of course, he's an icon. I compared him before to David Beckham in popularity.
"It doesn't surprise me but it's good to see how the people love him and how important he is for the people.
"I am happy to hear him telling you that he still wants to improve, be better and work hard. That mentality is fantastic and that is why he is a very good example for all the fans and all the people, not only here in Asia but in the world."
Son played down his importance to a squad he is proud to be a part of, but reminded his team-mates that, while they reached the Champions League final in 2018-19, they can improve having failed to deliver silverware despite showing significant promise for a number of years.
"It's not just me, it's everyone," said Son, shrugging off the accolades of his coach. "It's special being here with the team. I don't care about being the main [attraction] or not.
"I'm happy to be here but I'm still learning, looking to be better day by day. Of course, I enjoy it but not too much pressure. I should enjoy this moment.
"I should be proud to work harder than before because the people are always watching me and expect more. I'm looking forward to being better with our team and with our staff. I'm always looking forwards."