The loud booing that followed the announcement of Marsh's bowling spells appeared to be an expression of the Victorian crowd's disapproval that Peter Handscomb was dropped for the Boxing Day Test in his home state, with Marsh taking his position.
While it is more common to see a visiting player jeered by fans, it is rare to see an Australian player receive such a reception in a home Test.
"I don't think it's great," Head said. "Obviously we've seen it with Kohli as well but for Mitch, who worked his bum off today, I thought he bowled exceptionally well.
"I thought he created pressure in tough conditions and fought really hard. I don't think any Australian cricketer in Australia deserves to be booed.
"I understand the Victorian crowd, Petey obviously missing out, but I think it's pretty poor for Mitchy to cop that.
A Facebook page was set up ahead of the Test which encouraged fans to boo Marsh, who was the most economical of Australia's bowlers, conceding 23 runs off his 15 overs.
Marsh's bowling was cited by Tim Paine as a major factor for his inclusion and, on a flat pitch that yielded just two Indian wickets, his inclusion provided welcome relief for Australia's pace attack.
But while the crowd's reaction was impossible to miss, Head said he didn't believe Marsh was affected by it.
"I think Mitch is a character to get on with it," Head said. "As he showed., he did his business, he did his work, he bowled exceptionally well, did the job that was needed for the team and that's what Mitch has always done.
"He's always been someone to get the energy around the group, lead from the front and I think he did that and in tough conditions to grab the ball and bowl the way he did was really good. He created a couple of chances as well.
"I think the way he showed today, I think great team man, great fella, worked his backside off for the boys today and I think he did a wonderful job so yeah disappointing and hopefully that won't be the case for the next couple of days."