The 26-year-old goalkeeper raced out to challenge Romelu Lukaku for the ball during their stalemate at Goodison Park but received a nasty blow to the head from the Belgian's knee which left him knocked out.
However, Lloris insisted on carrying on for Spurs following the collision when it looked as if he was going to be replaced by Brad Friedel.
"He took a really bad whack and I was worried when he went down and stayed down," Dawson, the Tottenham captain, said. "When he got up his legs gave way but he stayed on and made two good saves.
"I lead those boys but safety is the most important thing. He was in a bad way but by the time he came around he was wanting to stay on. He's a little bit dazed but he's a lot better."
Spurs have since been branded as showing an "irresponsible and cavalier attitude" by a brain injury charity.