Butland could have kicked the ball out of play to receive treatment, but instead punted downfield and once Germany regained possession, Kroos drove forward and beat the stricken stopper with a low 25-yard shot.
Butland then had to be stretchered off and there are now doubts over whether he will play again this season or at Euro 2016.
"My nature to not give up was my downfall, the injury I'll recover from but more importantly the experience I'll learn from," he tweeted.
"Thank you for all your messages, I'll be having a scan today to see the damage to my ankle and will work hard to get back fit! thank you!"
England fell 2-0 down before staging an unlikely fightback in the final half-hour and beating the world champions 3-2.