"I thought we were in the game for a long time into the second half despite conceding that goal, which was a bad one to concede," said Hodgson.
"We got over that disappointment and got back into the game and looked like an equaliser might be on the cards."
Hodgson also praised Vardy, who he gave his international debut to during his time as England boss.
"I have always admired him as a player. He is a top-class striker," he added. "I actually thought we handled him quite well in the game but he is on the spot to take those chances and get over the 100 mark."