Rovers fought back after going a goal down with a brilliantly worked goal for Mame Diouf before the points were won by Andrey Arshavin's second-half goal.
"I'm disappointed we didn't get something out of the game and from my point of view the first half was our opportunity to get our noses in front," said Allardyce.
"Because we didn't take those opportunities we paid the price for that. At some stage Arsenal were going to take control of the game. You switch off for a split second and they are very, very good at punishing you.
"The pass and Walcott's finish were top quality and while we might try and criticise our defenders it's very difficult to stop that sort of quality of football."