The former Liverpool and England winger won 12 of his first 13 games as Hoops boss after being appointed as part of a “Dream Team” pairing with Kenny Dalglish in the summer of 1999.
But he saw his reign crumble after striker Henrik Larsson suffered a horrific leg-break in a UEFA Cup tie with Lyon.
The French giants ended Celtic’s European hopes before defeats to Motherwell (twice), Rangers and Hearts left them 10 points behind Dick Advocaat’s expensively-assembled side.
The axe was finally swung after Barnes oversaw the infamous Scottish Cup defeat to Inverness at Parkhead in February 2000.
Deila has endured his own struggles after watching his team spill 10 points in their opening eight Scottish Premiership matches as well as twice blowing chances to qualify for the Champions League.
Barnes is confident the former Stromsgodset boss can turn things around but admits the Norwegian is lucky the Ibrox club - now playing in the Championship following their liquidation saga - are not around to challenge.
Asked if he had any advice for Deila, Barnes said: “Win football matches. That’s the only thing you can do.
“You have got to have the character to win matches, but if you lose matches then of course you are going to be under pressure.
“I know myself because of the first 13 matches I had in charge up there, we won 12, but I was still under pressure. That was because Rangers were winning too.
“Obviously this season with Rangers not being there, you would expect Celtic to be right up there at the top but they are not.
“However, they have not even played 10 games yet. Yeah it’s disappointing they are not in the Champions League but Celtic will still win the league and win it comfortably, even considering the start they have had.
“Maybe things are going to be harder but I would still be very surprised if they don’t win the league, so I would urge the people up there to support Ronny.
“If he gets time, I’m sure he will do a good job. You are always going to be under pressure when you are manager of Celtic, particularly if you haven’t had the start that you would want.
“But I know he has got a good record and from what I hear he is a good coach.
“If he is given time I’m sure he will be successful, but obviously right now that start he has had is not the one he’d have wanted.”
Barnes’ Celtic reign lasted just 29 games as the fury from the Hoops faithful became too much for the Parkhead board to bear.
But the 50-year-old does not believe the flak being directed art Deila is any worse than the grief experienced by bosses down south.
Speaking ahead of the Hoops’ trip to face Ross County in Dingwall on Saturday, he said: “Is the pressure of managing Celtic unique? Not really. Just look down here in England and there are managers getting the sack after four games.
“Of course up there in Scotland right now with Rangers not being there, Celtic are expected to win every game and when they don’t, people will ask questions.
“But managers up and down the country are living under extreme pressure.
“When I was managing Celtic back in ‘99, maybe it wasn’t as prevalent then. But in 2014 people are losing their jobs after just a handful of games.
“I had something similar at Tranmere when I lasted 14 matches. Look at Huddersfield, they sacked Mark Robins one game into the season.
“Managers would get more time in the old days but this is what football has become. People have high expectations and you have to live up to them.”