The former Gunner was asked whether Southampton and West Ham can remain in the Premier League's top four this season and, in response, used the example of Forest.
The club won back-to-back European cups, among other trophies, under Clough over two decades ago and Keown feels it is becoming more and more difficult to replicate that success in the modern day.
As such, the former Arsenal defender feels what the Nottingham side achieved was 'astonishing.'
"I’ve been in to the boardroom at Forest and it’s quite surreal. It’s like a drinks cabinet you might see in a B&B. Those trophies are so iconic and part of their history and legacy," Keown said in a 'Tackle Keown' session with the Daily Mail.
"They should be displayed right at the front entrance for all to see, somewhere where they can inspire the next generation. Not hidden away.
"But it’s when you see those trophies tucked away you see how relatively small they were as club and just how astonishing their achievement was.
"The money involved now sadly makes it almost impossible for that to happen. Those clubs flew the flag in those days but it’s increasingly difficult for anyone to match those feats."
Forest fans wore green jumpers to commemorate 10 years since Clough's death a month ago in September.