Cahill was dismissed by referee Stuart Attwell after just 17 minutes of the game at White Hart Lane for a challenge on Scott Parker.
The Trotters had already gone a goal down when Gareth Bale scored and further strikes from Jermain Defoe and Aaron Lennon left them second bottom in the table.
Bolton manager Owen Coyle was furious with Attwell over the red card and marched across the turf at White Hart Lane to confront the official at half-time.
After the game the Scot said: "To say I am angry about it is a bit of an understatement.
"I am totally bemused by the decision. Maybe it was a free-kick or a yellow card, but not a red.
"If you understand the terminology it has to be a clear goalscoring opportunity. Now Scott Parker is a fantastic player but he took a touch with his left foot, went out to the wing, 50 yards from goal. We had Zat Knight in the middle and other defenders coming back.
"So there was nothing clear on a goalscoring opportunity. I think everyone in the stadium was baffled it was given."
Source: PA
Source: PA