Despite the loss Taylor was pleased with what he saw from his side after Barnsley scored twice inside the first 16 minutes at Oakwell.
Exeter have not won in six weeks, but the loss was just their third in that nine-game period, having drawn the other six.
He felt that after their shaky start Exeter looked solid, especially their injury-hit defence after a tough game at home to Burton Albion last Tuesday night.
“I can’t question the character,” he added.
“We’ll be hurting because we’ll know that that 10-minute period cost us another opportunity to pick up points.
“We were more than in the game apart from that period of play.
“It wasn’t brilliant, brilliant, brilliant, clean, clean, clean, cutting through us from Barnsley.
“With no disrespect it was a little bit of lower league football and we have to defend those moments.
“But at any level then if you don’t win a first contact and a second ball you’re going to be in trouble.”
