Republic of Ireland striker Stokes was turned away from the club’s training ground on Tuesday and handed a two-week suspension after tweeting his displeasure about not being included in Ronny Deila’s squad after travelling to Inverness on Sunday.
Stokes now faces a hearing which could determine his future at Parkhead but Allan has not engaged with the Twittersphere since his move from Hibs in August.
“I’ve not been on it since I came here, to be honest,” he said. “It’s probably a problem not worth having. I don’t need to go on Twitter and read negative stuff every day.
“That’s something I can do without. I’m glad I did it, it’s part of life for a lot of people these days, but it’s now something I can do without.”
Allan originally opened his Twitter account as a teenager at Dundee United but now prefers not to deal with online trolls.
“I was a young boy in Dundee, sitting in the house with all my team-mates,” he explained. “There was nothing else to do.
“Of course, it can be a good outlet sometimes but, for me, it’s something I don’t really need. Was it tough seeing the abuse I got when I left Hibs? Not really. It’s part and parcel of things. Obviously some of it is not nice but, if you want to be successful in football, then you are going to have to deal with a lot worse than that.
“I don’t know if I’ll ever go back on Twitter. Maybe, at some point in the future, I will.”