Jay Emmanuel-Thomas and Joe Bryan struck in the final 10 minutes to earn the Robins their first home league win since March 9 and inflict a fourth straight defeat on the visitors.
"For 80 minutes we did most things right. Unfortunately games last for 90 minutes," said Barker.
"If it had stayed at 0-0 it would have been a good game for us. But our decision making let us down with 10 minutes to go and poor defending cost us the opening goal.
"In the first half we were excellent and with better decisions in the final third we would have got on the end of something and taken control.
"We were beaten by a penalty on Saturday and a mistake here when we deserved something from both games.
"We just have to keep working and hope things turn for us, which I am sure will be the case."