Pochettino has guided Tottenham to a third successive top-three finish in the Premier League and has done so spending far less than the teams around them.
But without a trophy in his four years, Pochettino suggested that Spurs should “take risks” in the transfer market in the search for silverware.
The Argentine has been linked with a move to Chelsea since his comments, with the Blues looking to replace Antonio Conte at the end of the season.
And Rose, who last summer hit out at Spurs’ frugality, has urged chairman Daniel Levy to give Pochettino what he’s asking for.
“I have learned my lesson on speaking on that sort of stuff,” he said. “It is good that the manager has come out and said that.
“I hope the chairman can give the manager what he wants”
“I hope the manager, his coaching staff, the recruitment staff and the chairman can all come together and give the manager what he wants.
“I am fully behind whatever happens in the off-season.
“I hope we get some good recruits to help us push on and as the manager said the next step is to try and hopefully win something next year.”
Rose has been linked with a move away from Tottenham every since he criticised Tottenham’s transfer strategy last August.
The England left-back played second fiddle to Ben Davies for most of the season, making just 17 appearances.
But the 27-year-old has vowed to come back and fight for his place after the World Cup.
“It is a season where I have had to be patient and be mentally positive,” he said.
“Even though I haven’t played as much as I’d like I feel like I’ve grown mentally so there are positives to take out of the season.
“It is a team game. The first three years of the manager being here I have played just as many games as Ben (Davies) has, this season he has played a lot more than I have.
“It is just one of those things, I wish I could have played more, but you have two players to compete in each position and that is how I would want it at any football club.
“I fancy myself against anybody in the league.
“Pre-season; come back and hopefully me and Ben start from scratch and we start again and work hard to nail that number one spot.”