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.
The Gunners ended a run of four league games without victory as they won 2-0 at Bournemouth to go joint-second in the Premier League.
Mesut Ozil and Alex Oxlade-Chamberlain scored the goals midway through the first half on Sunday to move Arsenal above Manchester City, level on points with Tottenham Hotspur.
Manchester United remain fifth, six points off a Champions League place, after a 1-1 draw at champions Chelsea in the day’s other match.
Ozil put Arsenal in front after 23 minutes with an athletic, right-foot volley after a good header back by Olivier Giroud.
One minute later, Oxlade-Chamberlain rifled a low shot across the goal which went in off the post.
“We beat a good side, it was three difficult points but three very important points for us because we had not won for a while,” Arsenal manager Arsene Wenger said.
“We had a strong start, with good finishing and we controlled the game.
“We lost a bit of our urgency in the second half. We lost the killer instinct to get the third goal and on top of that Bournemouth are physically a strong team.”
Bournemouth enjoyed plenty of possession and Arsenal goalkeeper Petr Cech had to be alert to prevent the hosts from getting back into the match.
Bournemouth remain 15th, just five points above the bottom three, with manager Eddie Howe left to rue a slow start.
“We were much-improved in the second half without getting that goal to put them under pressure,” he said.
“We kept going, kept fighting, and if we had got that goal back with say 20 minutes to go, it would have made for an interesting finish.
“We got into some really good positions without the cutting edge we have had in recent weeks.”
United must have thought they had won at Stamford Bridge when they led 1-0 going into injury time thanks to a brilliant second-half goal by Jesse Lingard.
Lingard’s tight swivel and unstoppable shot was worthy of winning any game but Chelsea equalised in time added on through Diego Costa.
Spain forward Costa then almost won it for the home side with a fine strike from close range, but David De Gea blocked the shot.
Thibaut Courtois also had a good game in the Chelsea goal as the points were shared.
Chelsea remain in the bottom half, in 13th place.
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