Bates picked up a couple of bangs during the game and was eventually taken off 18 minutes from time.
Hoyte was limping in the last 15 minutes and at one time it looked as though he might have to come off, though he went on to finish the game.
Gareth Southgate: "Bates suffered from the impact of a tackle and we thought it was best to bring him off.
"We are assessing him and Hoyte, but hopefully it's nothing too serious.
"We need to keep all our players fit for the games which lie ahead of us."