Haddin questioned Gayle's value to the winless Thunder after a Big Bash League (BBL) season in which the 33-year-old international has scored just 70 runs in five innings.
Gayle responded on Twitter with "Not my fault he ain't good as I am even if I bat right hand".
The Thunder are already out of finals contention after losing their opening six games of the season.
Gayle said he had put his stoush with Haddin in the past, and was desperate to guide the Thunder to a win in Friday night's clash with the Perth Scorchers at the WACA Ground.
"It's just one of those things and I've put it behind me," Gayle said of his exchange with Haddin.
"I try not to be too negative for those sort of things.
"He's done his part and I've said what I have to say as well. That's it, and that's history."
The fifth-placed Scorchers (3-3) remain in the hunt for a semi-final berth, and will rely heavily on their opening partnership of Shaun Marsh and Herschelle Gibbs to get them off to a good start.
The WACA is familiar territory for Gayle after playing two seasons of BBL for the Warriors.
Gayle said he had fond memories of his time in Perth, and hopes his return will spark him and the Thunder back into form.
"We all go through these things as cricketers. It's nothing to beat yourself up for or worry about," Gayle said after landing at Perth airport on Thursday.
"You've just got to keep pushing and keep that self belief to get the job done.
"There's no pressure, to be honest with you.
"I have nothing to lose at this point in time, so it's a situation where we can go and express ourselves. It might just pay off."