Martinez's men have so far failed to recapture the consistent brand of football that saw them fall seven points shy of the UEFA Champions League qualification spot last season, languishing in 12th position this time around.
Everton have won just one of their past six league fixtures after losing 1-0 at home to Stoke City on Boxing Day.
That defeat left Everton 11 points behind fourth-placed Southampton heading into Sunday's trip to Newcastle United and Martinez is aware the Merseyside outfit must start collecting points sooner rather than later.
"I don't think in general we are lacking in confidence," the Spaniard said.
"I think the expectations, and the opposition giving respect when they're coming to Goodison has maybe played a bit of a part but I think it is a moment of the season that is pivotal for us to see how we can react.
"We have another game 48 hours later but when we assess the [Stoke] game it was a bit of an unfair reward in the performance of the two teams.
"I do think that reaction now calls for us to know what we're doing, we've got real understanding of how to perform and if we can keep doing that the results will come.
"Football gives you those sort of challenges and this is the challenge of the season.
"We need to make sure that we get through this period stronger than ever and that could really give us a strong second half of the season."
