The Latics head into Saturday's clash with West Ham having picked up just one point from their last five Premier League games.
Martinez claims they have been the victims of some debatable decisions, such as Arouna Kone having a late equaliser chalked off for offside in last week's 2-1 defeat to Swansea.
"We're really looking forward to playing at home, and the next game for us is vitally important, to be able to get all the good things together and to start getting the results we deserve," said the former Swans boss.
"Against Swansea we were a little bit disappointed. We worked really hard and you're not going to get many teams who go there and make more passes than the home team.
"But we had a period where we conceded two soft goals and then you're giving yourself a very difficult task. But the reaction was very, very good.
"That's the challenge - reflecting points in the good work the players are doing on the pitch, and that's where we are. We're not going to look away from the responsibility to try to correct that as quickly as we can.
"But I'm very excited, I'm very pleased with the signs we've shown so far and it's time to get a win and develop that into a very good season."
Martinez could be without Japanese winger Ryo Miyaichi for Saturday's match as he is struggling with a slight groin problem, while winger Albert Crusat (knee) and defender Antolin Alcaraz will definitely be missing.
Alcaraz has not played for Wigan since August after damaging his groin on international duty with Paraguay, and Martinez admits he has been frustrated by the pace of the defender's recovery.
The Wigan boss said: "At the moment he's where we expected him to be but I do feel he's still a long way from being involved in a match. Weeks more than months, but it's hard to tell.
"Antolin's such a quick healer that I felt probably we would have him quicker than any period the doctor could say, but at the moment it seems to be the doctor was right and we'll have to wait a few weeks. Probably before Christmas is about right."