Tottenham allowed Kyle Walker to leave for Manchester City for a fee which could rise to £50 million, whilst Nabil Bentaleb, Clinton N'Jie and Federico Fazio have also departed on permanent deals.
He went on to implore Spurs to sign "well-known" players and, relating to his contractual situation, 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.
Sky Sports News understands Rose would consider joining Chelsea or Manchester United.
"If you remember four years ago, the people say, 'Who is Mauricio Pochettino?' I'm sure they used Google or Chrome!"
Pochettino said that he has accepted Rose's apology and he reiterated that the club would sign players before the close of the transfer window.
Gayle missed the final two friendlies of pre-season due to these hamstring/confidence problems and only played 30 minutes of the third last one.
"And when I first arrived here [in England], people wanted to know who Mauricio Pochettino [was] too".
Outspoken pundit and former midfielder Robbie Savage has predicted Tottenham to start their Premier League season with a defeat against Newcastle on Sunday afternoon.
'Danny Rose is a fantastic player but he has been mishandled, whoever has advised him to do that is ridiculous. "It was like, 'Wow, how did he do that?' I mean signings like that are what we need - that's just my opinion". "I'm sure they used Google or Chrome!" former Argentina global Pochettino said.
"I am relaxed because when you see the team and the players they are so focused".
"I think the team are very united". "I don't want to compare us with other clubs who have made signings before us in the previous two seasons and we have finished above them".
Asked if he could influence what the players are paid, Pochettino said: "I'm not involved in negotiation, no".
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