Spurs had held an interest in the winger throughout the summer window, but the North London outfit failed to meet Villa's valuation of the youngster.
Bruce has acknowledged that Grealish is disappointed having failed to secure a move to the Premier League, but that the 22-year-old had accepted the reasoning given to him by the club.
At a press conference, Bruce told reporters: "I can understand there'll be disappointment from Jack but he's been very respectful.
"I understand his disappointment. Let's be fair, Spurs are a big club. He's taken the decision from the owner and hopefully he can move forward."
Grealish is expected to feature when Villa host Wigan Athletic on Saturday afternoon.