Cooley said he was hurt in the second quarter of Sunday's 27-24 defeat. He said the hit was a "little bit of a bell-ringer" but not forceful enough to knock him out.
"I came off the field and took a breath and thought 'Wow,' " Cooley said in his regular weekly appearance on 106.7 The Fan. "I've actually had a few concussions in the past -- I don't remember anything. I was totally there yesterday. I remember every part of the game. I remember all the plays."
Cooley said he passed "all the doctors' test and stuff" and returned to the game in the second half, catching two passes in the third quarter. He said he "didn't want to accept" that he was hurt.
"But as I kept playing, I started getting more and more of a headache," Cooley said. "And I was a little bit slow, and I went over to our trainers. ... I felt like stuff was happening way faster than I was happening. It just got to the point where I felt like I wasn't helping the team to be out there, and I definitely wasn't helping myself."
Cooley said he underwent a series of tests Monday and indicated he would have a CT scan on Tuesday. He must be symptom-free for two days before he can be allowed to practice, which means he might be able to play in this week's game at Chicago.
Coach Mike Shanahan said he wasn't certain when Cooley was hurt, but fellow tight end Fred Davis said it was a helmet-to-helmet hit.
"He was running a route, and a guy just ran straight into him with a head shot," Davis told Comcast SportsNet after the game.
Shanahan said the two-time Pro Bowl tight end was showing a competitive nature by continuing to play.
"Throughout my career, most people do try to do that," Shanahan said. "He's a competitor, probably didn't think it was anything big and wanted to go back in there. And we could see very quickly that something was wrong, and that's why he was out."
This was the second week in a row the Redskins have had a player suffer a concussion. Rocky McIntosh was hurt a week earlier against Green Bay and did not play against Indianapolis.