The Spurs chief controversially claimed winning trophies only serves to build ego after they crashed out the FA Cup to Crystal Palace.
That came days after losing in the Carabao Cup semi-final to Chelsea.
Pochettino said: “Again we’re going to have the debate whether a trophy will take the club to the next level. I don’t agree with it.
“It only builds your ego. The most important thing for Tottenham right now is to always be in the top four.”
But Dublin blasted the Argentine for his comments and told The Debate show: “I don’t understand that. I don’t understand a manager who can say that winning a trophy is all about ego.
“Why enter the competition in the first place if it’s not important to win trophies? I don’t get that mentality.
“I believe he’s upset about going out the two competitions, I think that’s got something to do with it.
“But I genuinely don’t believe that he believes what he said.”
Appearing alongside Dublin on The Debate was Chelsea Women’s boss Emma Hayes, who defended the Spurs chief.
“He has to say what he said because the realities are the team are three weeks away from a £1billion stadium opening,” she said. “There’s a bigger picture at stake.
“You don’t want to go into a £1billion stadium at the end of the season in the Europa League.”
Pochettino made seven changes to his side against Palace which included Christian Eriksen not even featuring on the bench.
But the Spurs boss stuck by his selection and said: “Regrets? No, no. We played with our best team that we can play at the moment. I think it was a moment, of course, for different players to play. To help the team.
“I think we came from a very crazy fixture and were forced to take some decisions, rest some players and rotate. But we are going to play Wednesday too and Saturday.”
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