Beavon was stretchered off after 20 minutes of a feisty goalless stalemate following a clash of heads with Orient defender Nathan Clarke that prompted a lengthy stop in play, but Grayson confirmed Beavon was up and about soon after.
Without Beavon leading the line, Preston could not find a way past inspired Orient goalkeeper Jamie Jones, who produced a string of fine saves to deny Jack King twice and Nicky Wroe late on.
Orient rarely threatened and as a result saw their three-match winning run come to an end, while Grayson was left frustrated his side could not collect a third win on the bounce at Deepdale.
"Beavon got a knock to the head, I think he was knocked out for a small period, but he came round and watched part of the second half," said Grayson.
"We'll assess him over the next few days, he seems to be ok. I suppose it looked worse with the brace, but when somebody's knocked out you don't know what could happen, but we went in at half-time and he was having a shower.
"Through good defending, being brave, and us being not as clinical as we should be, we weren't up a couple of goals at half-time.
"We've taken another point, kept another clean sheet, and drawn a game we could have easily won.
"With some of the opportunities you can't understand how they didn't end up in the back of the net, but at least we created them.
"Eight or nine times out of 10 we would've won that game with the chances we created."