Tottenham Hotspur face United in the FA Cup semi-final at Wembley on Saturday, both teams seeking their final hope of silverware this season.
Mourinho's side moved six points ahead of Spurs in the Premier League table on Wednesday with a 2-0 win at Bournemouth, but the United boss has come under criticism after conceding the title to rivals Manchester City.
"For me, Jose Mourinho is one of the best managers in the world," Pochettino told reporters. "He does not need to show anyone that he is one of the best.
"Manchester United are having a fantastic season. Like us, they are disappointed to be out of the Champions League because it is massive for them and for us.
"We are similar. They are better than us because they have more points in the Premier League. He is doing a fantastic job in his second season in Manchester."
The winner of Saturday's game will come up against either Chelsea or Southampton in the final, which takes place on May 19.