The Goodison Park side moved to within a point of fourth-placed Arsenal - with a game in hand - after a 3-0 victory over the Londoners last weekend.
Victory at Sunderland on Saturday will lift Everton into a Champions League spot and, despite suffering a 1-0 home defeat to Gus Poyet's side on Boxing Day, Martinez is confident his players will cope with the pressure over the remaining fixtures.
"We said our target is clearly in the final third of the season of going into every game to try to be as good as we could and get as many points as we could get, and that doesn't change," he said.
"I think what it changed last Sunday is probably the perception from the outside and the understanding that we've got mathematically a great opportunity with six games to go, but internally it doesn't change anything.
"We've got terrific competition for places. The players are looking fresh, they're looking in a very good moment of form, and we're just looking forward now to facing Sunderland.
"That is going to be such a difficult encounter at their own ground, and we still remember the defeat we had at home against them and we need to make sure we are ready and prepared to perform as well as we can."