ITV Football tweeted "bye bye Celtic" after the Parkhead side was drawn to play four-times Champions League winners Barcelona, Benfica and Spartak Moscow in the group stages.
Celtic manager Neil Lennon raised concern and supporters tweeted their disgust at the tweet.
Lennon said: "I think ITV owe us an apology."
One fan said: "I assume @itvfootball also think Man City have a very tough draw. But no 'bye bye Man City' tweets. Interesting."
Manchester City were drawn in the so-called "group of death" with Spanish champions Real Madrid, Dutch league winners Ajax and German Bundesliga victors Borussia Dortmund.
Another fan added: "A disgraceful and disrespectful comment made in relation to Celtic in Champions League. I will no longer watch ITV Sport."
Later, ITV Football deleted the offending message and tweeted: "To Celtic fans out there – we mean no disrespect. An ill-advised way of us saying we think you've got a very tough draw. Apologies."
But the Celtic manager appeared to believe that was not good enough, tweeting: "Not happy with that." Earlier, he said the draw was a "marvellous day for the players" and watching it was a "magnificent feeling".
Celtic won through to the lucrative group stages for the first time since the 2008/09 season with a 4-0 aggregate win over Swedish champions Helsingborgs.
Elsewhere, Champions League holders Chelsea were drawn against Italian champions Juventus, Shakhtar Donetsk and FC Nordsjylland. Arsenal are to play Schalke 04, Olympiakos and Montpellier.
Sir Alex Ferguson's Manchester United will face Braga, Galatasaray and FC Cluj.