Views from Thordarson and King following Saturday's draw
"I was very disappointed with the first half, we didn't start well," Thordarson admitted after the game.
"I could see their goal coming. Our commitment and work rate were not good enough and there were strong words from me at half time.
"We were far better in the second half, deserved our equaliser and should have won and I am not happy with just a point.
"Now I am looking for a performance that lasts 90 minutes and not 45 minutes at home."
Swindon boss Andy King said: "We looked very comfortable in the first half and scored a very good goal to get our noses in front.
"But I didn't recognise us in the second half. We lost our shape; we played far too deep; and individuals did not do their jobs properly.
"In fact we suffered a bit of a pummelling but we managed to maintain our unbeaten away record against a hard-working Barnsley side who, let's not forget, are up there with us in the top five or six.
"Indeed, although Barnsley will feel they should have won because of their second half pressure, we still could have nicked the three points.
"Parkin was adjudged offside early on when he was clearly behind two Barnsley players and Tommy Mooney sent a golden opportunity against the post in the last minute.
"We could quite easily have had a penalty as well, for what appeared a clear push on Mooney by their skipper."