Carvalhal was appointed Swansea City manager days after leaving Sheffield Wednesday.
Carvalhal has won four and lost one of his seven games in charge of Swansea, who he joined just days after leaving Wednesday by mutual consent on Christmas Eve.
Almost unthinkably, the Welsh side's form has seen them off the foot of the Premier League table and into 16th position, although they are still just a point above the relegation places.
And Palmer - who followed Carvalhal's Sheffield Wednesday reign closely as a former player at Hillsborough - has told the Ref Show that Swansea's situation would not look quite so rosy had the Portuguese not entered a pressure-free environment.
"He’s had a tremendous start," said Palmer of Carvalhal - who was appointed on an initial six-month contract. "And I think also, you have got to be a bit careful with this. I think he was given the job on the [basis] of he could get them promotion out of the Championship [next season] - so they are playing without fear and that’s a different prospect. If he was brought in to keep them in the division, and the pressures that go along with that, I think you’d have seen a different scenario. He's was brought in [with] nothing to lose.
"I’ve seen Swansea play two or three times now I’ve never seen him play that adventurous when he was at Sheffield Wednesday - by the way I’m not having a dig at Carlos, I thought he did a fantastic job - but in the end he was negative in his approach.
"He’s been very positive with his approach with Swansea and that’s because he’s got nothing to lose. And it’ll be interesting when it comes down to the last few games whether he still continues with that approach, because if he does they’ll stay up. If he reverts to what he did at Wednesday they’ll go down, and that’s when the pressure’s on."
As fate would have it, the draw for the FA Cup fifth round saw Swansea paired with Sheffield Wednesday, and sees Carvalhal return to Hillsborough this coming Saturday.
Will Carvalhal keep Swansea City in the Premier League?