Browns President Paul Holmgren told reporters team medical staffers had their attention trained elsewhere when McCoy took a helmet-to-helmet hit from Pittsburgh Steelers linebacker James Harrison in a Dec. 8 game.
Harrison, a repeat offender for delivering dangerous hits, was suspended for one game by the NFL.
Holmgren said by the time medics reached McCoy, he was lucid and not exhibiting any signs of a concussion, so no sideline tests were administered, The New York Times reported.
The quarterback later re-entered the game, which the Browns lost 14-3.
His father, Brad McCoy, Tuesday criticized the team for putting him back into the game even though he had knocked unconscious. Holmgren and head Coach Pat Shurmur have said Colt McCoy didn't show any concussion symptoms until after the contest.
The quarterback was diagnosed with a concussion the day after the game.
No one who saw a video replay of the hit immediately told medical personnel of its severity, he said.
"It seems inconceivable, but nobody alerted anyone," Holmgren said.