Everton welcome Stoke to Goodison Park on Boxing Day on the back of a disappointing 3-0 defeat to Southampton last Saturday.
That loss marked Everton's fourth in six games in all competitions and left the Merseyside club a disappointing 11th in the Premier League table.
Martinez's men are 13 points worse off than they were at this stage last season, which saw them finish an impressive fifth.
Now they face another stern test against a Stoke side that has claimed away wins at Manchester City and Tottenham and a home victory over Arsenal.
The Spaniard is wary of the threat posed by the Staffordshire club but is eager for his side to bounce back and put a performance together.
"Against Manchester City and Arsenal they showed what they [Stoke] are capable of. They are going to be really tough opposition," Martinez said.
"I think they've found a way of playing that is attractive to watch. It's one of those teams that has been under a real transition under Mark Hughes. They're very, very difficult to play against.
"The last few games, they've been very unfortunate in their last few results. I admire the way they've been progressing this season.
"We've got three games in six days which is an incredible opportunity. Everybody is expected to perform. The fans are the first ones to support us, we've all got to put it right together."
However, the hosts are still without a number of first-team players, with Leon Osman and Kevin Mirallas (both ankle), James McCarthy (hamstring), Tony Hibbert (knock) and Darron Gibson (knee) all unavailable.
Stoke, meanwhile, could be without striker Peter Crouch due to a neck problem, while Marc Wilson (knee) could again join Victor Moses (thigh), Stephen Ireland, Peter Odemwingie (both knee) and Dionatan Teixeira (foot) on the sidelines after missing Monday's 2-0 home reverse against Chelsea.
Hughes' men have now won just one of their last six games, a run of form that has seen them drop to 13th in the table.
And, with fixtures against West Brom and Manchester United on the horizon following the trip to Everton, Hughes has conceded that he will need to rotate his squad if Stoke are to get back to winning ways.
He said: "We are trying to look after people and give them the best chance to play to their maximum."
Stoke have risen to the challenge against some of the league's better sides this term. If they can do so again then the visitors promise to pose a tough challenge to an Everton team struggling to meet the high standards set by Martinez's early success.
