The Toffees were drawn to face the current Premier League leaders in the two-legged last four tie after the pair navigated past Middlesbrough and Hull City respectively in the previous round.
The first leg is due to take place at Goodison Park on January 6, before the return game at the Etihad Stadium on January 27.
And Martinez is of the opinion that his side has what it takes to reach the final – despite wanting his players to put the matches to the back of their minds for the time being.
“At this stage of the competition you don’t expect any easy draws,” the Spaniard said.
“Getting into the semi-final in the manner that we did is a really good sign.
“We are very excited about the draw and we are looking forward to it. We are feeling good, playing really well and we are confident of enjoying the two games against Manchester City.
“If you want to go all the way in any cup competition, then you get to a point where you have to play against the best, and clearly Manchester City are one of the best teams in Europe.
“So it will be a phenomenal football occasion for our Club – but we’ll put it aside for now and we’ll enjoy it when the first leg comes round.”