Spurs, who have yet to make a new signing this summer, have been interested in a move for Grealish for several months but only recently made Villa an offer.
With the window closing two days before Spurs play their opening Premier League fixture against Newcastle, Pochettino looks set to enter the season with the same squad as finished the last one.
That led to Spurs becoming the first Premier League club to go through a summer transfer window without additions since its introduction in 2003.
"Of course it's hard to understand for people in football that Tottenham didn't sign or sell players, but sometimes in football you need to behave differently", he said.
"The club is doing an wonderful effort to try to finish the stadium as soon as possible, and the lodge finished at the training ground".
"I was so clear with everyone", Pochettino said.
Asked why the club have struggled to recruit players this summer, Pochettino replied: "The market was insane".
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Alderweireld's teammates Danny Rose and Mousa Dembele were also expected to leave the club this summer but failed to get their moves over the line before the transfer deadline. We didn't sell players and with 25 in the squad it is hard to add.
"Our targets are always in the same level of Real Madrid or Manchester United or Manchester City, but for different circumstances we can not achieve that". If we are happy with our squad and can not improve our squad, sometimes it's better to keep our squad together.
"I am not anxious, I am not sad, I am so happy". I think the club made a massive effort to try to extend contracts with people like Harry Kane.
Tottenham "achieved their objective" and did a "great job" by keeping their best player in the transfer window, says manager Mauricio Pochettino.
"I am so happy in the way they come back to training on Monday".
He said: 'Being fearless is the most important thing. If all the players today are thinking about a collective target, we can be competitive.