Forest won the league by seven points in 1978 in their first season after promotion and went on to triumph in the European Cup in the following two years.
O'Neill, currently manager of Ireland, compared Leicester's 3-1 away win over title rivals City to an equally stunning success just before Christmas 1977 when the Forest team he played in under Brian Clough won 4-0 at Manchester United.
"We scrambled up from the old Second Division in third position and up until Christmas time people were saying our bubble would burst," he told BBC radio's Sportsweek programme.
"It never did. The Old Trafford game was really something special and you can compare this great result for Leicester at the Etihad."
Rated as 5,000-1 outsiders before the start of the season after avoiding relegation last May, Claudio Ranieri's side now top the table by five points with 13 games to play.
"While the other teams are faltering, as well as being involved in other competitions, they just keep going on," said O'Neill, who is in San Francisco with his Ireland assistant Roy Keane to watch the NFL Super Bowl.
"When you are opening up a gap and games are running out, you've got to give yourself a chance. They are winning games with less possession than the opposition but that has continued month after month.
"If ever there was an opportunity, this is it. And it should give hope to every other team."
Leicester, managed by O'Neill from 1995-2000, play away to another of their title rivals Arsenal next Sunday.
(Reporting by Steve Tongue, editing by Alan Baldwin)
