The veteran winger admitted that the Hammers made it tough for them throughout the game, and credited substitutes Michael Carrick and Paul Scholes with turning the match around.
"In the FA Cup anything can happen so we are pleased to get through. Some players are coming back from injury which can be tough but they did well," BBC Sport quotes him as saying.
"West Ham are a tough team to play against. We couldn't get out of our half at the start of the second half but we kept it better when Michael Carrick and Paul Scholes came on. If you don't enjoy nights like this you never will."
Giggs went on to say that he has yet to decide whether to retire at the end of the current campaign, insisting he is still enjoying his football.
"I don't know if I'll have another year, I'm enjoying it now and we'll see what happens," he added.
Wayne Rooney scored the only goal of the game early in the first half but missed a penalty late in the second after Jordan Spence was penalised for an alleged handball.