The Welshman, who was booked for diving, will miss the second leg of the tie because of his disciplinary record in the Europa League this season.
However, the Spurs manager told reporters after the game: "With this result we would have asked him to get a yellow card to be clean for the last eight.
"We are in a good position but it is not finished, so we will miss Gareth. He has been influential in consecutive games but hopefully we can make it without him.
"He is a tremendous player, so obviously he is going to be missed, but an opportunity might arise for another player."
The suspension means Bale with have a clean disciplinary record should Tottenham secure a place in the quarter-finals of the competition.