The midfield duo signed on transfer deadline day, with McCarthy commanding a £13m fee from Wigan Athletic and Barry joining on a season-long loan from Manchester City.
The Portuguese coach is preparing his team for a tough test at Goodison Park in this evening's 5.30pm kickoff, and believes that the Toffees present a more potent threat on their home patch.
"Everton is a good team," Mourinho told reporters. "Goodison Park is a difficult place to play. Their record at home is normally better than away.
"I watched in my study time twice the game Everton against Chelsea from December, and the three points came in the wrong direction. They were better than Chelsea in that match, so it is difficult, but in this league no match is easy.
"They did very well in the last days of the market. They got two very good players for midfield, different profiles, ages, futures, but [Gareth] Barry is a very good experienced player and [James] McCarthy is a good young player."