The Celtic boss had suggested that the Tony Macaroni playing surface was behind the US defender being ruled out of the midweek Champions League tie with Real Madrid, which resulted in a 5-1 defeat for the Scottish champions.
Postecoglou stated: "The artificial pitch wasn't great for him, so we left him at home."
Martindale, however, is less convinced and called for evidence to back up the claim.
He said: “I can’t speak for the medical staff at Celtic, but what are we basing this on? The park’s too hard? The park’s too soft?
“Where is the assumption coming from? I don’t know.
“Surely you can’t just say that because it’s plastic you pick up more injuries.
“Yes it’s different, but what is the difference? It would be good to get a study on that.
“I look at the hybrid pitches and there are a lot of injuries happening on them because they’re very hard and there’s not a lot of give on them.
“If you look at the English Premier League, when someone scores and does a knee slide, there’s never a divot.
“I get Ange’s frustration, because they’re elite level and we’re not.
“If I could have Motherwell’s surface and a training facility, I’d take it all day long over the plastic. But do I think it leads to recurring injuries? I’m not so sure.
“I think sometimes it can be an easy rationale as to why someone is injured.
“Where are all my players’ injuries from playing and training on a plastic pitch?
“And if it’s because of a change of surface, why am I not picking injuries up when we play away on grass parks. It’s up for debate.
“And where do Celtic B play their games? On a plastic park — so it can’t be that bad.
"What is it about a plastic park that supposedly leads to more injuries? We have an £80,000 shock pad under our surface — these are the things that people don’t know.
“If you were to do tests on grass, hybrid and an astro with a shock pad, I’d like to see what it comes back with.”