Shiels' men are chasing a top-six finish and a win at home to the Buddies would have left them just a point away from achieving their goal.
But Esmael Goncalves put St Mirren ahead and, although Kris Boyd levelled just after the break, Killie could not get a winner and now need to beat bottom club Dundee at home on Saturday to clinch a top-half berth.
St Mirren are only 10th in the standings themselves but Shiels rates them highly and was pleased with his side's display.
"We did exceptionally well against a team who, if we do make it into the top six, we won't find a harder opponent than," he said.
"They have got quality right through the team and people have to start recognising teams like St Mirren.
"If they can keep their team together, they have got a great chance of making Europe next season. I'm really impressed with St Mirren and I'm glad we were able to match them.
"In the second half, we looked the more likely side to score. I don't know if their goal was offside but that is not relevant now."