Allardyce, who made nine changes to his team, said after the game: "I told everyone after the Swansea match that we would change the team in terms of the players we would need to use to make sure we had enough fresh legs to come with a very difficult game.
"Burnley are top of the Championship and they beat QPR comfortably 2-0 on Saturday. We played on Sunday afternoon at four o'clock and got back late on Sunday night, so it would have been ridiculous of me not to use the players who were fit, eager and raring to go and remiss of me not to play some of the Under-21s who are top of their league and test them at this level.
"Getting the result means I've done my job the right way and that's what I'm paid to do and have to do, irrespective of what everybody from outside West Ham says in terms of what needs to be done.
"The players have paid me back in terms of what needs to be done because the first half wasn't very clever. We had to reshuffle and the defence was there again. We've now played six games away from home and conceded just one goal, and even that was from a penalty that wasn't a penalty.
"We had a back four for the last 20 minutes that included Leo Chambers, Pelly Ruddock and Dan Potts and had Joey O'Brien, a full back, at centre half. They defended against Sam Vokes and Danny Ings, who have scored nearly 20 Championship goals between them.
"Jack Collison, Stewart Downing and Kevin Nolan all lifted the team in terms of possession when they came on and we started passing the ball properly in the right areas, getting in and around Burnley and showing their defensive weaknesses.
"Eventually we got two penalties and they clinched it. It was a well deserved victory in the end and a really good performance that has got us into the quarter finals."
Sean Dyche saw his Burnley team lose for the first time since the defeat at Brighton in August. "We haven't had that feeling for a while, but I felt the lads did well and delivered a good performance, particularly in the first half, against a group of Premier League players and a big club," he said.
The first of the penalties that beat us, awarded by referee Bobby Madley against Jason Shackell, looked, at best, a soft award and Sean Dyche was certainly unhappy with it. He added: "To have the game change on an incident like that one is disappointing.
"The referee felt he got the decision correct, but my view is that I didn't think he had a good enough view. That is more my concern and it's a soft one in my opinion, having seen it again. The contact is minimal because the defender has every right to get across and challenge for the ball.
"I thought the referee had a very tough view. He is a long way behind the incident and with three or four players in between. I questioned whether he could be 100 per cent sure there was no contact with the ball.
"I think Shacks has done well to get across Nolan and get a block on it. You can't actually see it that clearly, but it looks like there is some sort of contact by the angle the ball travels, so we are disappointed.
"I just asked him if he felt he had a good view and he said he thought it was a definite penalty, so we accept that and we move forward."
Then came the second spot kick. On that he said: "We are scrambling to get back in the match and Keith has clipped their lad in the box on the breakaway. It's a penalty and a red card, and it's the latter that really hurts us. I'm not sure you need a red card for that, even though the law says you have to."
Away from the penalties, he added: "I think we have given people plenty to smile about here lately, so I don't think anyone is over thinking tonight. I like winning and so do the players, it's as simple as that, but if you are going to lose then lose in the right fashion, and I thought we did that.
"There was no shortage of effort or application and good quality, so there are many good signs because the players who came in tonight did very well. We had four players out tonight and we are hopeful they will all be back for the weekend, so we are ready to go again."