Pompey have lost four of their last five matches, leaving them 19th in the Championship.
But Dubov insists Cotterill, who guided the club to 16th last season despite their off-field woes, is the right man for the job.
"We support him and believe in him - his talent, his attitude and his work," Dubov told The News. "We understand it's difficult for the fans to understand where we are right now.
"Of course, we ourselves want to be in the top part of the table, not the bottom. But we see the progress of the team and we understand there's a long way to go and it's not going to happen in one day.
"Every day our staff prepare for us a list of things from Facebook and Twitter, so we know what the fans are saying. We support Steve and all our staff from the first day they come to the club to their last."