Manager Mixu Paatelainen reiterated his demand that his Dundee United players improve as they build up to Saturday's Premiership visit by Ross County.
But former club skipper Maurice Malpas fears the public berating might damage the confidence of the younger players.
"I never identified any individuals. I was critical of the whole squad," said Paatelainen on Tuesday.
"We don't tolerate performances like that. The things that we didn't do right were very basic. I was very annoyed with that and I still am.
"The players know that and agreed with that.
"I felt sorry for our supporters who travelled to the match and saw a performance like that.
"I don't think the players will suffer confidence-wise at all. They realise it, they feel it."
Paatelainen's first match in the Tannadice dugout was a 1-0 home defeat by Hearts. The mauling at Celtic leaves the team at the bottom of the Premiership on five points, half the total of second-bottom Partick Thistle after 12 games.
As United get ready for the weekend, Paatelainen added: "The important thing is that we learn.
"The team has been making mistakes throughout the season and that is why we are where we are in the league table.
"If you concede two goals or more on average per game you are asking too much for your offensive play to win a match.
"Every successful team does the fundamentals right. At the moment we are too weak in defending."
Having scored nine league goals, United are on a par with fellow strugglers Motherwell and Partick Thistle, but those two have lost 15 goals compared to United's 26.
Asked if the Tannadice job was the hardest of his managerial career that has taken in Hibs, Kilmarnock and the Finland national team, he replied: "I don't know if it's the toughest, but it's certainly a tough one. Things are not great.
"We have a big challenge on our hands. We must stay patient and keep the confidence as high as possible.
"It's going to be a long season for us, a long battle.
"Some experienced heads will come in once the injury list improves. Through time we will try to improve the squad by bringing in new players. The chairman indicted there is a possibility of doing that.
"Some players will have to leave, but that is natural."