Mutko's comments follow a decision by the IAAF to uphold the ban on Russia's track team from international competition.
The IAAF banned Russia in November 2015 for widespread drug use, and said on Tuesday (AEDT) it is unlikely to reinstate the team until November.
That means there will not be an official Russian team at the world track championships in August, though there may be "neutral" athletes competing.
"There were many abuses and breaches. Athletes broke the rules and many coaches don't understand how to work without doping and it's high time for them to retire," Mutko told state news agency R-Sport.
"But over the last year, colossal work has been done."
On Monday, Mutko was singled out for criticism by IAAF taskforce leader Rune Andersen because of his often-colourful criticism of anti-doping rulings against Russia.
Following a council meeting, the IAAF laid out a series of conditions for Russia to return to competition, including the reinstatement of the national drug-testing agency, which remains suspended over various allegations of covering up doping.
Russian track federation vice president Andrei Silnov said progress was being made, but questioned whether the country's problems were as serious as the IAAF says.
"It's all being solved, slowly but surely. We're doing what we need to do," Silnov said.
"They say we have a culture of doping. What culture of doping?"
The IAAF is also considering 35 applications from Russians willing to compete as "neutral" athletes if they can show a record of independent drug-testing by agencies other than the suspended national body.
Two others - doping whistleblower Yulia Stepanova and US-based long jumper Daria Klishina - already have this right.
Silnov said he was opposed to the idea of neutral athletes in principle and might have refused the status during his career as an Olympic gold medal-winning long jumper, but said he would accept others doing so if there was no other way to compete.
"They're Russians regardless," Silnov said. "There's no other way out of this (situation)."