An independent commission found City guilty of charges relating to breaches of Premier League financial regulations between the 2009-10 and 2017-18 seasons.
The Premier League said the commission had found that the club arranged "sham" commercial deals with a number of sponsors as part of a disguised funding scheme.
Manchester City have rejected the findings and said they intend to appeal, arguing that the commission's opinion contains what they describe as material errors of law, principle and fact.
Burnham said the club should have the opportunity to challenge the decision through the available process.
"I think it's only right to say that it is still contested now," he said.
"The Premier League proclaimed (Everton) guilty and I never accepted that and therefore it would be somewhat wrong of me to leap to judgment on another football club.
"But they're very serious charges, don't get me wrong."
Burnham has previously campaigned on behalf of Everton, his own club, following the points deduction imposed on them for financial rule breaches.
He said that experience was one reason he did not want to make an immediate judgment on City's case.
"I remember people proclaiming Everton guilty at the time," Burnham said.
"And with hindsight, I think more people would say that wasn't fair the way that was handled. So it would be wrong of me to leap to one side given the experience that I'd had before becoming prime minister."
The Prime Minister also defended his record of dealings with Manchester City while serving as mayor of Greater Manchester.
Burnham has praised the investment made by City Football Group and the club's wider ownership in the area around the Etihad Stadium and across Manchester.
Asked whether those dealings would stand up to scrutiny, he said: "Oh indeed, I do actually thank the City Football Group and the wider ownership for the money that they didn't just put into the Etihad and the campus around it but also into the city, but yes of course."
He also said he would be concerned if City's owners ultimately decided to sell the club.
"I would be really concerned to lose them," Burnham said.
"They've been such a huge partner in the building of modern Manchester.
"Obviously, the building of Manchester City into the global force that it is."
However, Burnham stressed that he would maintain his distance from the legal and disciplinary process.
"I am not getting directly involved in the process. I've not spoken to anybody directly about that," he said.
"I have to keep my distance from it. It would be wrong for me to do anything else. It's an independent legal process that has to play its course through."
Burnham was also asked whether he believed Manchester City should face relegation but declined to give a view.
"There’s a lot at stake. Let's be honest about that, for the football club, for City supporters, for the city of Manchester," he said.
The Premier League has said the question of sanctions will be addressed separately following the commission's guilty findings.
Manchester City are expected to appeal the verdict, meaning the disciplinary process remains ongoing.
Burnham's comments therefore focus on the need for the appeal process to run its course before any final conclusions are drawn about the club's future.