The 30-year-old ace has come under huge scepticism from fans and pundits alike of late, with his place in the Hammers starting line-up now under threat following an impressive display from Adrian at the weekend.
Hart was forced to watch from the sidelines as he remains on loan from Manchester City and cannot play against his parent club, in a match that ended 2-1 to Pep Guardiola's side as Nicolas Otamendi and David Silva scored.
It could see Adrian retain his starting spot on Saturday as the Hammers face Chelsea at the London Stadium, and Kirkland backed former Shrewsbury Town ace Hart to overcome the criticism and be a better player for it.
"There seems to be a vendetta against him at the minute," one-time England international Kirkland said. "He is a top, top 'keeper. The criticism Joe has taken is very, very harsh but we all know the industry that we are in.
"You've got a target on your back and unfortunately it stays there for a while but Joe will fight this all the way."
Hart has conceded a huge 30 goals in just 14 Premier League matches this season, keeping only three clean sheets as he looks to find a permanent home after being ostracised by Pep Guardiola in the summer of 2016.
It saw Hart move on loan to Serie A side Torino where he performed admirably behind a leaky defence, and he will be hoping he is given another chance with the 2018 World Cup just around the corner.