The Merseysiders travel to the DW Stadium on Wednesday night in good form having won their last three Premier League games, including an impressive 2-0 triumph over champions Chelsea on Sunday.
Hodgson's side made a poor start to the season but have since hoisted themselves out of the relegation zone and Martinez feels if the Latics are to halt the Reds' momentum, they will need luck to be on their side - something that seemed to desert them in their 2-1 defeat at Blackburn on Saturday.
"It is probably the worst moment to play them," Martinez said. "Looking at the Liverpool side now, they play with huge energy and confidence - they were a joy to watch against Chelsea and you can start to see Roy Hodgson's hand on that side.
"Sometimes in football you need to be lucky and have a little bit of luck when you play the top sides, it is really important.
"I think we need to carry on with what we are good at, be stubborn, show good arrogance on the ball and make sure that we show we are playing at home.
"On the other side you need to understand that you are playing against an outstanding team with fantastic talent, and they are in a very good moment of form.
"That always has to be in mind, and it would be a big difference playing Liverpool six weeks ago to playing them now.
"But we are ready and we are hurt from what happened at the weekend.
"It is the moment not to drop our standards and make sure we change that feeling around the football club quickly."
Charles N'Zogbia had what would have been the opening goal disallowed at Ewood Park for an apparent foul in the build-up, and Martinez feels his team - currently 18th in the table and winless in four league fixtures - have had their progress hampered by misfortune.
"If we had been a bit more lucky with decisions we could easily have been 10th or ninth in the table," the Spaniard said.
"I would never tell you that I have been unhappy with the level of performance.
"I think it is very important to understand that sometimes results don't reflect performances, and at the moment I have been very pleased with the performances, apart from the Fulham game (a 2-0 defeat at Craven Cottage). We need to carry on with that."
For inspiration, Wigan need look no further than last season's 1-0 home win over Liverpool, although Martinez is keen to stress Wednesday night's opponents are not the same outfit as before.
"You need to remember there is a different manager in charge for Liverpool and they do things slightly differently - those little things are important," Martinez said. "But it has been mentioned at the training ground about what happened last season and the feeling we had.
"It was probably one of our best performances in the last campaign in terms of a total, complete performance and that is something we are capable of doing."