The 30-year-old could do little to stop Dempsey's 12-yard volley today and put in an impressive display in front of the hostile away following in the second half.
Grant paid tribute to the former Norwich stopper's character following the draw.
Grant said: "Rob Green is a good goalkeeper. Every press conference I get asked: 'how is Robert Green?'.
"He was good and every player sometimes has bad moments. Some players have it in the middle of the season. He had it at the start of season. It's only because of the World Cup that everyone is speaking about him.
"He was a good goalkeeper and still is. His performance was good, and his character was good too."