Everton head into Saturday's clash at Goodison Park looking to arrest a run of four straight league defeats that has seen them drop to 13th in the table.
There were signs of recovery in Tuesday's 1-1 FA Cup draw with West Ham, in which Romelu Lukaku scored an injury-time leveller.
Manager Martinez is hoping that performance can spark an upturn in league fortunes and the Spaniard is confident of ripping up the form book against Manuel Pellegrini's side.
"We need to take responsibility," he said. "We're playing at home, we've had four bad results and we need to put that right.
"It doesn't matter what kind of opposition you're playing.
"Looking at our position in the league all we want is to get momentum and to do that you need a little chain of good results.
"Man City could follow the performance we put in against West Ham."
Martinez, who is without Sylvain Distin (groin) but welcomes back Leighton Baines (knock) and Antolin Alcaraz (suspension), is aware that stopping City will be no easy task.
Pellegrini's side have won 11 of their past 12 matches in all competitions - a 2-2 draw with Burnley on December 28 proving the only blot in that run - and they now have an identical record with Chelsea at the top of the table.
Even more ominous for Everton is the fact that City's top scorer Sergio Aguero and striker partner Edin Dzeko have returned to training.
Argentina international Aguero strained knee ligaments in the reverse fixture with Everton - which City won 1-0 at the start of December - while Dzeko has been absent for a month with a calf complaint.
The pair are in line to return to the squad this weekend as is captain Vincent Kompany (hamstring) and the trio's availability is a timely boost with midfielder Yaya Toure having departed for the Africa Cup of Nations with the Ivory Coast.
City are reportedly set to further bolster their wealth of attacking options with the signing of Swansea City striker Wilfried Bony and the champions appear well set for a sustained assault in their title defence.
Certainly confidence at the club appears high and midfielder James Milner - whose double helped City avoid an FA Cup upset in a come-from-behind 2-1 win over Sheffield Wednesday last Sunday - is targeting overtaking Chelsea.
"Hopefully we'll be looking to open up a little gap of our own," he said in the aftermath of the Wednesday game.
"All we can do is concentrate on our games and if we can get the results we want to get, it depends on how Chelsea do."
