With the Hammers leading 2-1, Taylor had a great chance when put through on goal to extend the lead but was denied by keeper Hugo Lloris.
Spurs then scored twice to secure a 3-2 winat Upton Park, and Allardyce admits that he is disappointed by the result.
"We've done a terrific job and made a terrific go of it. Jussi [Jaaskelainen] played so well," Allardyce told Sky Sports News. "It was at a crucial stage when Matt Taylor got through one-on-one. The 'keeper made a good save, but we want to be scoring that and, at 3-1, there's no way back for them.
"It's a very disappointing end to one of our best performances here against a top side. We caused them a lot of problems.
"We went 1-0 down to their first shot on target, got 2-1 up, had a chance to get 3-1 up, and then paid the price."
West Ham travel to Stoke City on Saturday.