Martinez could become the first manager to win the famous trophy in successive seasons with different clubs.
The Spaniard defied all odds and led Wigan Athletic to claim the cup last year for the first time in the club's history but after they were relegated from the Premier League, he left to take the reins at Everton.
McCarthy, who also left Wigan for the Toffees at the end of last season, is adamant that his manager's pleasing track record of late means he has the ability to put up a strong campaign for the cup.
"You always want to win cup competitions and last season I did that," said the Republic of Ireland midfielder. "Now each and every one of us wants to do it at Everton.
"We want to lift trophies and qualify for Europe. There's a real buzz about the place, around the city, and hopefully we can keep that going.
"The gaffer has been there and done it. You want someone in charge who knows what it takes to win the cup, and even better he's done it so recently."
On Saturday, after the Blues' 4-0 victory over QPR in the third round, McCarthy said he was impressed with how his team played against the Championship side.
"We've got a good squad and at this moment in time we're looking strong," he added to the Liverpool Echo. "I think with the window open, the manager will try and add another couple and hopefully we don't lose too many.
"We were class all over the pitch, keeping the ball and closing them down. At times, we split from the centre-halves and played out from the back and we created chances while limiting them to hardly any.
"We were always in control of the game and although we knew it could be a tough game, we had a right go.
"The way we kept the ball was brilliant and then won it back when we needed to by pressing them high. That's the main thing the gaffer wants to see at the club. Recently, it's really starting to show.
"We get it down, knock it about and keep believing we can go places."