Furious supporters nicknamed him the "Argentinian David Moyes" following Tottenham's shock FA Cup defeat to Crystal Palace.
Third-placed Spurs are still in the Champions League and face another trophyless season after going out of the Carabao Cup to Chelsea on Thursday, but Pochettino claimed winning silverware would simply just build egos at the club.
He 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 now is to always be in the top four."
The Argentine chief, 46, has emerged as the favourite candidate to take over from Ole Gunnar Solskjaer, 45, at the end of the season.
But United fans on Twitter claimed the former Southampton manager is not the right man for the job.
One said: "The absolute state of this Argentine David Moyes. Do we really want a manager with this mentality at United?
"Personally, I don't want him anywhere near Manchester United next season. Just give the job permanently to Ole."
Moyes, who was sacked by United after less than one season in charge, was renowned for his lack of confidence in the club.
He once claimed United should aim to play like arch rivals Manchester City and labelled his team as underdogs against Liverpool.
He said: "I think we've played a very good side [City] and it's the sort of standard and level we need to try and aspire to get ourselves to at this moment in time."
Ahead of the Liverpool game in 2014, he claimed: "Their league position suggests they're ahead of us. They possibly do come here favourites."
While another added: "What is Pochettino talking about? Every season is about winning a trophy or trophies.
"This causes me more certainty I don't want him managing my team United. It also shows why Spurs are always going to be second best if they are never even looking to win anything."
Fans urged the club to offer Solskjaer the job on a permanent basis following his record-breaking start at Old Trafford.
The Norwegian boss has won eight games on the bounce since he took over from Jose Mourinho in December.
United face Burnley at home on Tuesday after Friday's remarkable 3-1 win over Arsenal in the FA Cup.
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