Celtic have not won in West Lothian since Livingston returned to the top flight in 2018, drawing three times and losing once in their four trips.
Martindale had his tongue in cheek when he repeated criticism of their artificial pitch but he acknowledged it was a factor in Celtic's struggles.
And with Postecoglou having suffered five defeats in six away matches as Celtic manager, the latest a 4-3 Europa League reverse against Real Betis on Thursday, Martindale has vowed to pile on the pressure.
"They are going through a transitional period, albeit they are a very, very good football team," Martindale said.
"But there's probably a lot of football players, and the manager, coming into the unknown a little bit.
"Hopefully everybody has told them how horrific the park is and they are looking forward to it.
"Within these four walls, we are expecting to go and try and pick points up on Sunday.
"I have got to try and use every advantage I have got. The park is obviously horrific, which helps us.
"But, listen, they have played a hard European game and from my point of view, the game went very well in our favour because it was a really, really difficult game for Celtic, albeit they were very, very good in moments of the game.
"But the way the game went, you could see they were putting a lot into the game, there was a lot of energy, and the temperature obviously (didn't help).
"I don't know when they travelled back but all these factors and variables can only help us on Sunday and we have got to try and use that to our advantage.
"We were talking about that in the office the other day. Historically, and I'm not just looking at Celtic, when teams have played away in Europe there is always a wee bit of a lull when they come back to their domestic leagues. So I think we have got to utilise that as best we can."
Livingston have shown they can get results at Celtic Park as well, securing two goalless draws in the past three years, but Martindale feels home games have a different dynamic.
"You've had Brendan Rodgers, Neil Lennon has been here," he said. "It's a nice stat to have.
"But let's be honest, the calibre of player that Celtic can afford to put on the field, I don't think they enjoy playing on a plastic surface. Let's be honest. So I have got to use that to my advantage."