Tony Pulis admitted his side were well beaten by Champions League chasing Man City after watching another defeat for the Baggies.
Albion's 3-1 reverse at The Etihad Stadium was their sixth defeat in eight games and means the Baggies have one only once since March.
Robson-Kanu came off the bench to score a late consolation on an evening when Albion struggled contain a fluent City side.
"They deserved to win tonight," Pulis said afterwards.
"Once they got their noses in front, they're a difficult team to pull back.
"The two quick-fire goals killed us. When the third one went in, you're looking down the barrel.
"Today we were second best, there's no doubt about that against a very good side."
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