Western Bulldogs forward Ugle-Hagan responded to last week's vile racist attacks by lifting his jumper and pointing to his skin, recreating Winmar's iconic gesture during Thursday night's win over Brisbane.
It came almost 30 years to the day since Winmar stood up to racial abuse from Collingwood fans at Victoria Park in April 1993.
"I'm proud of Jamarra for standing up for himself," Winmar said in a statement on Friday.
"It's up to the new generations to reinforce the stance I made back in 1993.
"I'm still here, still involved with the issue, but it's been 30 years now.
"It's like a big relay race, time to pass on the baton."
Winmar thanked Bulldogs coach and former St Kilda teammate Luke Beveridge for supporting Ugle-Hagan this week after the 20-year-old was racially abused during and after his club's round-two defeat to the Saints.
The 57-year-old has seen some improvement in attitudes since he was subjected to racial abuse during his playing career, which ended in 1999.
But he warned racism is still an issue in the AFL and Australian society.
"Things are getting better, with increased awareness, and kids are getting educated in schools now about racism in sport and in society, which is great," Winmar said.
"There's still a few who can't control their negative attitudes, all we can do is keep supporting each other, and keep calling it out."
Ugle-Hagan recreated Winmar's famous gesture after the first of his five goals against Brisbane, equalling a career-best tally.
"I also want to congratulate Jamarra for his outstanding on-field performance," Winmar said.
"Five goals, keep up the good work!"
Winmar, who started his career with WAFL club South Fremantle, played 230 AFL/VFL games with St Kilda and 21 with the Bulldogs during a decorated career.
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