Asked if Tottenham's players understand the lack of new arrivals, Pochettino responded: "They don't need to understand".
The bid from Spurs has been rejected, and Villa any further bid - be it from the North London club or any other team - will also be rebuffed.
Chairman Daniel Levy has proved his point by refusing to sell to Belgian to another Premier League side, but Spurs still have the option to sell him overseas.
Spurs will be desperate to be one of the main challengers for the Premier League title next season as they look to try and win their first trophy under Mauricio Pochettino.
Pochettino says he is glad to keep his Spurs squad together amid speculation surrounding his stars.
The window remains open to European clubs until the end of August, so there is still the possibility of players going out even after the English deadline passes.
Mauricio Pochettino has told Danny Rose, Toby Alderweireld and Mousa Dembele to forget about their futures and concentrate on Tottenham.
The alternative is to re-integrate Alderweireld into the Tottenham squad, and start making him a key player once again. "I am the boss and if I expect from you to do something, then you need to provide it".
"It's true our targets are always the same level as Manchester United, Manchester City or Real Madrid but for different circumstances we can't achieve that".
"I am so happy with the way they came back to training on Monday".
"I am not anxious, I am not sad - I am so happy", said Pochettino.
"Of course people in football find it hard to understand that Tottenham didn't sign or sell players, but sometimes in football you need to behave differently".
"If you cannot add players who can improve your squad, the most important thing is to make sure you do not lose your best player".
But Pochettino believes all three are at risk of losing focus and has urged them to forget about their futures and contribute to Tottenham's season instead.