The 19-year-old, who is on loan from Hull, was shown a straight red when he caught Will Haining in the 64th minute.
It came after Townsend had scored his first league goal with a super free-kick to cancel out Chris McCready's headed opener.
Chesterfield coach Mark Crossley said: "He's gutted, he's only had two league games and he's learning the game. If you know him as a person, you know he didn't mean to do it.
"He did catch him but I wouldn't say it was malicious because he's not a malicious player. If you do catch someone with your elbow, it could be a yellow but unfortunately it was a red. I don't think we can argue even though we know Conor didn't mean to do it.
"We are disappointed with the sending-off but credit has to go to our players that when we went down to 10 men we kept trying to win the game. Tommy (Lee) made a miracle save at the end so looking at it overall, it was probably fair."