The closing stages at Easter Road saw Ryan McGivern cancel out Sammy Clingan's opener, before the visitors immediately regained the lead through Jude Winchester.
And less than 60 seconds later Leigh Griffiths completed the scoring, tapping home from close range.
Shiels claimed that while it was a great game of football, his players were disappointed not to have taken three points having held two late leads.
"I thought we had it won when we scored the second goal," said Shiels.
"I thought it was a great game of football. We took the lead right after half-time. All our kids, who did a great job tonight, were involved in the goal and it was a great finish from Sammy. We hit the post and looked like we were going to add to it.
"We dropped off, gave them the pitch but they didn't look like they were going to hurt us apart from corner kicks.
"We knew that corner kicks were going to cause us a problem because of their superior physique after all the injuries that we have had. We were lacking height and they got their equaliser.
"We then went up the park, regained the lead when young Jude Winchester rifled it in.
"Then it was a foul on James Dayton, I think, but referees are only human and they didn't spot it. The players are in the dressing room gutted."