Having lost three of their last four Premier League outings, Spurs find themselves 12th in the table after 11 games, albeit still only four points shy of the top four.
Dawson, who left Tottenham for Hull City in August, saw several managers come and go at White Hart Lane during his nine-and-a-half year stay, and the 31-year-old wants the club to give Pochettino a chance.
"They have to be patient," the defender told The Express ahead of the Premier League meeting with Tottenham at the KC Stadium on Sunday.
"It takes time when you bring in a manager and he brings different players in. He will have a different style of football.
"I have seen a few off in nine-and-a-half years at Spurs!
"I never thought I would be there that long when I moved from Nottingham Forest. It was an amazing time and it was emotionally hard to leave.
"It was made clear I would not play as much football as I would like under Pochettino. When the chance came to come to Hull and I could see what they were building last year and with getting to the [FA] Cup final, I was delighted.
"I have huge respect for Spurs and still have a lot of friends there.
"I keep in touch with lots of people and it was a sad day to leave, but I am looking forward to playing against them and being able to thank the fans, who were fantastic to me, through some hard times."
