Town manager Joe Royle conceded that West Ham had deserved to win the play-off second leg at Upton Park, his side having had an off night.
Royle said: "We had a poor night. Players froze but over the course of the season they've done us proud.
"We've played some terrific football and scored a lot of goals this season but tonight we didn't perform to the level we can.
"I could be critical of them but on the night that just wasn't us.
"We had our moments but realistically that's just clutching at straws because West Ham were stronger throughout.
"We had a clear cut penalty turned down and Darren Bent should have given us a lead in the first couple of minutes.
"But, I can't be too hard on the lads, they're an honest bunch and have given me everything.
"Their million-pound players up front were the difference."
Hammers' boss Alan Pardew was understandably pleased to reach the play-off final: "We've had one of those seasons that has been ever so tough.
"Everyone knows our problems - they've been well documented but we've kept strong.
"On the performance tonight, no one can say we didn't deserve to win 2-0.
"We put a lot of work in in preparation. The atmosphere was tight and I'm pleased with the way we dealt with it.
"People have looked at our team and accused us of certain things but we've come through it. We've enjoyed the evening but know the job's not done yet.
"We're playing for the biggest prize in English football but the players have got to play with freedom.
"For a club of this size, we we want to get into the top six of the Premiership and we have taken one step towards that."