Barnsley boss Danny Wilson says his players, despite being told, did not expect Chester to be so good in their FA Cup second-round tie on Sunday.
but Conference club Chester twice had attempts cleared off the line and also hit the crossbar.
League One Barnsley are currently 47 places higher in the football pyramid.
"If they underestimated Chester I think the first 30 minutes showed that. You prepare the players as best you can but it's between the ears," said Wilson.
"They have to take the bull by the horns but didn't do that at all."
Chester, who pulled off an unlikely result by in round one, were close to causing another upset at Oakwell.
"Kane Hemmings had a chance late in the first half that could have changed the match," Wilson told BBC Radio Sheffield.
"But credit to Chester. People scoffed when I said they were a good side. The Conference gets underestimated because people haven't seen it. Until they see it in front of them they don't believe you - they do now."