The Toffees made it five wins in a row at Craven Cottage on Sunday to close to within four points of the UEFA Champions League places with a game in hand and a visit from Arsenal to come next weekend.
Martinez's men are very much in the hunt, and the Spaniard believes it is results such as the one secured in the capital in their latest outing which has the Merseyside outfit daring to dream.
Everton did not have things all their own way against rock-bottom Fulham, but a dogged second half display saw their substitutes make the difference as Steven Naismith forced an own goal from David Stockdale and netted the third himself after Kevin Mirallas had responded quickly to Ashkan Dejagah's leveller.
Martinez told Sky Sports on the importance of a hard-fought success: "It was vital. I do believe that these are the games that allow you to achieve aims or not.
"They are not the games with the glamorous opposition at home, but they are the type of games that, for one reason or another, can see the opposition stop you from being yourself and you can't be bright enough to use what you normally use and you drop points in moments like today.
"Then you need to understand that this is the stage of the season against a team that is fighting against relegation, I know it from my own experience that it can be quite difficult.
"So for us to be able to get five straight wins I think reflects the character and the work that these players have been putting in on a daily basis and I couldn't be prouder of them."
While the introduction of Naismith at the interval helped to turn the tide in Everton's favour, the fact that Ross Barkley had to be withdrawn to make way for the Scotsman offered cause for concern - with the England international nursing a calf complaint.
Asked for an update on the midfielder's fitness, Martinez added: "He's good. You need to understand that Ross has got a great frame and sometimes when you get a knock on soft tissue in such a demanding week, you are going to suffer.
"But in some ways he is a quick healer and we just hope he can be back for next week."