Pochettino, now in charge of Tottenham Hotspur, was 34 when Valverde made the decision and retired shortly afterwards.
But speaking before Barca take on Spurs on Wednesday night, Valverde said he holds Pochettino in high esteem.
"When you're a coach, you have to make decisions, always trying to choose the best players for your team," he told a news conference. "I've had to do it over a long time. Mauricio has also had to make his own.
"I made the decision to do without Pochettino. He has also had to make some [decisions] that someone wouldn't like. We have a good relationship and we respect each other."