The Manchester United striker was dismissed for kicking out at defender Miodrag Dzudovic after 74 minutes with the score at 1-2. While England were able to hold their lead for the final 25 minutes, Montenegro's Andrija Delibasic snatched a draw in the final seconds.
The tie was enough to seal the Three Lions' place in next summer's finals, but Cahill conceded that it will be difficult without the "phenomenal" striker in the team for even one game.
"It will be a massive blow with the talent Wayne has," he said. "He is phenomenal. It is going to be a big blow at the finals.
"Going down to 10 men was tough but the main thing was we got the job done in difficult circumstances.
"When something like that happens, you've got to deal with it and carry on and that's what we did."
England goalkeeper Joe Hart later described the referee's decision to send the striker off as "pathetic".