McCarthy came in for criticism last month for sending out a virtual reserve line-up against Manchester United at Old Trafford.
But the former Republic of Ireland manager is to choose his line-up from the players who performed creditably against Liverpool and Manchester City during the festive period even though both games ultimately ended in defeat.
Wolves, currently lying in 15th spot, visit the Hammers next Sunday before tackling Wigan at Molineux the following weekend.
McCarthy said: "It is an important game on Sunday. We want to win it. I will be playing as strong a side as I can play.
"I am playing the first team. We want to win it because we need to win a game.
"We have just lost two on the bounce against Liverpool and Man City despite playing well and maybe the results don't mirror the performances.
"It doesn't give you any momentum for the Premier League but winning a game won't do any harm (before next weekend) and I don't see a cup run doing us any harm either.
"Winning is a great habit to have. We've had a good run before the last two games. It always feels a better place when you have won a game, no matter who the opposition are."
McCarthy admitted: "I haven't seen Tranmere yet until I see the DVD tomorrow. But I have scouts who watch them.
"They have had a difficult start. They have picked up in the last month and so they have a bit of momentum behind them. We want to beat Tranmere."
Wolves will have to contend with the game kicking off at 6.15pm on Sunday evening to accommodate coverage on the Football Association's website.
McCarthy has sympathy for the fans who will have to make the trip to Merseyside but has no problems with the unusual timing from a playing point of view.
He said: "I've had some kick-off times. It's a new one for me. I haven't done it before. I'd be more than happy to be playing 3pm tomorrow afternoon.
"But that is the way it is. The games get moved. It is not our decision to question why. We just go and play.
"We are in the FA Cup, we are invited in the competition every year, and we go and play when they say. I've got no issue with it.
"Maybe it makes it a bit more difficult for fans. They are going back to work on Monday and would prefer to have played Saturday, have a couple of pints, Sunday off and back to work on Monday."
McCarthy would like to strengthen his squad during the next month but is adamant there is no imminent activity in terms of players moving to Molineux.
He said: "Is there any transfer news? There isn't any. None at all. As I sit down here today, there is absolutely none."
David Jones, George Friend and Sam Vokes, who has returned from his loan spell at Leeds, have been added to the squad on duty against Roberto Mancini's side.
Wolves 8/11, Draw 5/2, Tranmere 4/1