Rose said last week that he couldn't wait to retire from football due to racism. He was one of a number of England players who were racially abused against Montenegro last month.
Townsend said: "Danny's a very brave man for coming out, being so honest and speaking the truth. Obviously I sympathise with him; we all support him.
"Luckily so far I haven't experienced racism but I know Danny has on more than one occasion. He's experienced it with the England U21s and the seniors in Montenegro the other day.
"We need more players like Danny to come out, be honest and speak the truth, to say what they really feel. Danny's an incredible person - hopefully the system can help Danny and he can enjoy his football again."