Rose also suggested he does not earn his full worth under Tottenham's wage structure and questioned the depth of quality in Pochettino's squad - remarks he apologised for on Friday.
The Colombian is set to cost Tottenham £35m should they decide to move for the 21-year-old and although Spurs are yet to make a signing this summer, Pochettino was quick to state that he is not fearful of the lack of new faces this summer.
England global Rose was forced to apologise to the club in a statement published shortly before Pochettino's pre-season press conference, after he gave an interview in which he attacked Tottenham's rigid pay structure and careful transfer strategy.
"I don't think it's a matter to joke about because some of the global players today, maybe one or two years ago, none of us knew them very well".
When you sign players like Eric Dier, who are internationals today, nobody knew him.
Spurs are yet to buy any new players in this transfer window and Rose, 27, told The Sun they needed to sign "world-class players" and "not players you have to Google and say, 'Who's that?'"
"Also, when I first arrived here, people wanted to know who Mauricio Pochettino too".
Daniel Levy is claimed to be in Amsterdam attempting to seal a deal for the 21-year-old Columbian who has two global caps.
The Argentine said ahead of a Premier League opener against newly-promoted Newcastle on Sunday: "Always in my life I try to win".
"You need to understand that he [Rose] gave his opinion", he continued.
"I'm not anxious", he said.
"As a Tottenham player I'd love to see more signings".
Mauricio Pochettino has seen Manchester rivals United and City spend big this summer but claims Tottenham are trying to "win in a different way". We were focused from the beginning of pre-season to challenge and try again to prepare ourselves to compete in a very tough league.
"The fact of the matter is, Danny Rose can ask to leave the football club - there's no problem with that and it's happened historically in the game - but the way in which you go about it in a respectful manner is important, I think".
"I think the team are very united".
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