Friend was due to take charge of Monday night's crucial match at the Britannia Stadium but was taken off the game after Spurs supporters protested on social media he was a Leicester fan.
Neil Swarbrick will now referee Tottenham's fixture while Friend has been moved to Manchester United's game at home to Aston Villa.
Wenger said on Friday morning he felt the decision was wrong, as it questions the professionalism of referees, and Pochettino admits he was also surprised at the change.
"We never complain and I want to say we trust in all the referees but I think we need to trust," Pochettino said.
"In some point I agree with Arsene
It is important to keep the integrity of the referee and always back the referee.
"They are human and can make mistakes like us but it is important next time to behave naturally and to show the referee the trust and respect.
"Then whatever happens in the game, on the pitch we are human and can make mistake and not because something is going on behind."
Pochettino's men play the Potters eager to close the gap on Leicester, who are seven points clear at the top of the table with five matches left to play.
Crucial to Tottenham's remarkable title challenge has been the form of Toby Alderweireld but the Belgian was a surprise omission from the PFA Players' Player of the Year shortlist announced on Wednesday.
Pochettino, a former defender himself, admits forwards receive more recognition but says he does not underestimate Alderweireld's contribution.
"Football is to score goals," Pochettino said.
"But for us like a manager it is very important for me the keeper and defensive line are in the same level of importance of player.
"I cannot do anything about this because I am not involved in the selection of the players.
"There is no defensive player on the list and I have nothing to say but I am happy with him.
"His performances have been fantastic from beginning of the season and he doesn't need to be recognised to feel that."
Harry Kane is fit after overcoming a dead leg he sustained against Manchester United last weekend while Clinton Njie is also available again after recovering from a knee problem
Nabil Bentaleb, however, has a knee injury and is out.
Source : PA
Source: PA