Branislav Ivanovic headed the visitors' winner eight minutes from time just moments after Jason Roberts had spurned a clear chance to put the home side back in front.
Allardyce said: "They've got a punishing side to their game and they're ruthless. When they're being out-played - and we out-played them at times - they hang in there.
"They're not in the game and they're not looking like scoring and we're in the ascendancy, then with three passes it's a goal. That outstanding quality can punish you at any time."
Allardyce, whose cause was not helped by first-half injuries to Gael Givet and goalscorer Benjani Mwaruwari, added that he could have few complaints about his side's display.
"It's one of those days where you play as well as you possibly can. It's pleasing to create chances against such a big team but it's the ultimate kick in the teeth when you don't take them."