Dyer's injury-time goal, which equalised Shane Long's second-half strike, was his first goal in top flight football since May 2007.
Redknapp said: "It was a bit late. I tried a few different players today but couldn't really see the goal coming. We were a bit short really.
"It was a good finish from Kieron. He got through a full game which was good. He's kept going. He hasn't played a full game since I don't know when.
"I didn't want to get beat. It was important to stop getting beaten. The draw today, following the win against Chelsea, is not bad. West Brom are not a bad side. They are strong, well organised with a bit of flair. You can see why they are in the top half of the table."