Cahill was dismissed just 18 minutes into the match after a challenge on Scott Parker near the half way line was considered by the referee to be the denial of a clear goal-scoring opportunity for the Spurs player.
But Coyle was disappointed by the decision, claiming that Zat Knight was providing cover, but even if he had not been it was too far from goal to warrant such a punishment.
“Well I’ve got to say, I think that the word harsh is an understatement,” he told BBC Radio Five Live.
“It was an incredible decision. And obviously 17 minutes into the game it gives you a mountain to climb, especially when playing against one of, with Manchester City, the top teams in the Premier League at the moment.
“I’m totally bemused by the decision. I mean the terminology we use is 'a clear goal scoring opportunity' and Scott Parker was 50 yards from goal on a wide position. He’d flicked the ball past Cahill, but Zat Knight was inside.
“I accept that it is a foul and probably a yellow card, but for that to be a clear goal scoring opportunity – I’m totally baffled. Even if there is nobody else on the pitch, I would still suggest 'clear goal-scoring opportunity'...how do you explain that?”
“In my opinion, it was a wrong decision. As soon as I can appeal it, the appeal will be going in. The whole stadium and even Harry [Redknapp] himself, which does not normally happen with opposition managers, thought that it was such a travesty, it was incredible.”
But the former Burnley manager has reminded his players that if they are to improve on their poor performances of late, they will have to be prepared to work hard.
“It leaves us two points from getting ourselves out of the bottom three,” he continued.
“But the bottom line is that if you want to feel sorry for yourself you’re not going to do anything about it. But if you’re prepared to commit, work hard believe in your own ability and that of your team-mates, there is no doubt that you can sort it out and start moving up that league table.”