The Bosnian, who has been a frequent substitute this season, netted the game's only goal in the first half as City beat Albion 1-0 at the Etihad.
City had a number of opportunities to put the game beyond the Baggies' reach, but Dzeko was happy to win against a difficult Midlands outfit.
"In the first half, in the last 25 minutes in the first half, we had four or five very good chances and scored only one goal," Dzeko told Sky Sports News. "In the second half it was a very open game as well, they had chances and we had some chances.
"I think it was a very tough game. I can speak for myself and say I was very tired at the end of the game. I can't remember the last time that I played 90 minutes."
City now turn their attention to Wembley, where they face Wigan Athletic in the FA Cup final on Saturday.