He went on urge Spurs to sign "well-known" players and added: "I know my worth and I will make sure I get what I am worth".
Under chairman Daniel Levy, Spurs have tended to sign young players with potential, including Rose himself in 2007, or foreign players untested in English football - an approach supported by Pochettino.
"I don't think it's a matter to joke about because with some of the global players, maybe one or two years ago, none of us knew them very well".
His apology came hot on the heels of a number of reports claiming that Rose's departure could provide a mass exodus of Tottenham's best players, who would all stand to earn considerably more away from north London.
"When you sign players like Eric Dier, who are internationals today, nobody knew. or Dele Alli who was in League One or Kante", Pochettino said.
"If you see the squad, it is obvious that we need a striker".
Outspoken pundit and former midfielder Robbie Savage has predicted Tottenham to start their Premier League season with a defeat against Newcastle on Sunday afternoon.
"I know Danny Rose". When I play with my son or my wife, I try to win. I'm just not buying the idea that we don't need anyone.
"I've never seen him be upset about the (lack of) signings either around the players or around the training ground. When you see the team so relaxed, calm and focused for the game on Sunday, I feel how can I be nervous?"
Mauricio Pochettino has joked that Harry Kane is tiring of being lavished with praise by his Tottenham boss. You [the press] have access to the other players so you can ask them.