The Goodison Park club currently have the joint-highest number of draws in the league with six along with West Brom and have taken a point in each of their last three games, including Saturday's thrilling 3-3 Merseyside derby against rivals Liverpool.
But Martinez feels now is the time to start racking up maximum points if Everton are to remain in contention for European competition.
"We've had three very good performances but we need to add points," he said.
"All the points we've had this season, we've deserved. None of our points have been fortunate. At times we've suffered the opposite.
"The team now is ready to score goals against anyone. The players know that. We are balanced and capable of controlling games.
"In the derby we showed a bravery but it was a controlled bravery.
"What we want to do is to work a little bit harder, try to get an even better average in the next 15 games and make sure we get into the final third of the season with the biggest possible number of points.
"We need to push ourselves to fulfil our potential."
Martinez also moved to praise striker Romelu Lukaku, who netted twice in Saturday's derby.
"Romelu is such an intelligent person. He always knows how to behave in a situation. He has been very level-headed this week," he continued.
But Martinez refused to be drawn on reports linking him with a loan move for Seattle Sounders attacker Clint Dempsey.
"We will be linked with many players," he said.
"We will look at opportunities but now is not the time to talk about these things."
Everton currently sit seventh in the Premier League having lost just one match this season ahead of Stoke City's arrival at Goodison Park on Saturday.
