Team general manager Ed Hervey says staff will monitor Reilly's progress and then make a determination when — or if — he comes back this season.
"They're going through the (concussion) protocol for the rest of the week and we'll (then) make that determination," Hervey told a news conference Monday at Commonwealth Stadium.
Reilly, 28, went down with a minute to go in the first quarter of Saturday's 34-22 loss to the Toronto Argonauts at Commonwealth.
It came from a hellacious, and illegal, hit by Argo defensive end Cleyon Laing as the Esks were driving for a touchdown.
Reilly took the shotgun snap and was immediately flushed from the pocket.
He ran left, then cut right and headed up the middle, but was caught by Argo linebacker Robert McCune and defensive end Ivan Brown.
They had Reilly in a vise and were pulling him to the ground when Laing charged in from the backside and drilled his helmet into the back of Reilly's helmet, causing Reilly's head to snap violently forward.
Reilly lay motionless on the turf for almost 10 seconds while receiver Nate Coehoorn looked down at him and frantically signalled the medical staff to come on.
Reilly said he was never unconscious while on the ground and on Monday said he didn't know what Coehoorn was so concerned about.
"You'd have to ask Nate. I don't know," he said.
By the time staff arrived Reilly had staggered to his feet, looking dazed and a bit disoriented, waving away one of the trainers and taking a deep breath.
Reilly told reporters Monday he felt fine after the hit.
"I felt great," said Reilly.
"I was more concerned about the rest of my body than my head.
"I didn't feel like there was any head issues. I felt very clear. I was able to talk to the medical staff about anything that was going on. I had no headaches, no dizziness, no confusion. While I was on the field I felt 100 per cent mentally like I was able to play."
Reilly was assessed for about a minute and given the green light.
He said he felt clearheaded enough to take in the next play via the headset in his helmet, read the defence, adjust the throw for a press defence, and toss a 17-yard fade route to Shamawd Chambers in the end zone for seven points.
"I felt great about my ability to assess the play and executive it properly," he said.
During that play it Laing got free again, looping up the middle to drill Reilly in the shoulder as he threw. Reilly said it was a hard hit but did not contribute to the concussion.
He said he began feeling the effects of the concussion when he went to the sideline while the special teams kicked the extra point.
"When the first symptom popped up, at that point they (the medical staff) shut it down and said, 'There's no chance you're even getting close to the field,'" said Reilly.
He said he has felt good since the hit, has not had nausea or headaches.
Reilly, head coach Kavis Reed and Hervey all stressed that training staff relied mainly — and properly — on Reilly's responses to questions to keep him in the game.
"Our training staff has followed every protocol in regards to this matter," added Hervey.
"The player showed no signs (of concussion) at that time, and we stick by that.
"We would never put a player in jeopardy here in Edmonton."
The CFL has taken an active approach in the last two years to reduce concussions in the league.
League-issued guidelines stress that players who take severe shots in the head and neck be assessed for 12 symptoms, including dizziness, disorientation, or confusion.
Staff are urged in those situations to always err on the side of caution and pull a player.
The medical community is stressing the dangers of allowing players with concussions to continue playing because of second impact syndrome.
"Sometimes experiencing a second concussion before signs and symptoms of a first concussion have resolved may result in rapid and typically fatal brain swelling," reports the website from the internationally recognized Mayo Clinic in the United States.
"It is important for athletes never to return to sports while they're still experiencing signs and symptoms of a concussion."
Michael Copeland, the CFL's president and chief operating officer, said the league believes the Eskimos followed proper protocol in diagnosing Reilly.
"The trainers were right out on the field immediately after the hit, he said. "The trainers assessed the player, they asked him questions about head and neck pain, they asked him questions about headaches and he responded that wasn't experiencing any of those.
"It was only until after the subsequent play, which got a lot of attention because he threw a touchdown pass, when he was on the sidelines that he first raised the issue of perhaps having some concussion-related symptoms. At that point they did the right thing in removing him from the game, which is what our protocol requires the medical staff to do. They did follow all the right protocol."
Copeland added the CFL brings its medical personnel together at the league's annual congress each winter to discuss injury protocol as well as health-and-safety issues.
"I can tell your our medical staffs are incredibly engaged," he said. "These people are motivated and driven by their own professional responsibilities and requirements.
"They look at these things very very closely and I think in this case they followed their normal procedures which you would expect them to do."