The Austrian Under-21 international curled a 20-yard shot past Potters goalkeeper Asmir Begovic to give his side the lead in the first half.
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The youngster, who is a product of the club's academy, looked to have won the game with the second goal of his career only for Robert Huth to grab a share of the spoils late on.
McLeish told reporters: "Goals talk and it will be hard for me to leave Weimann out. It was a fantastic strike. We needed a bit of inspiration at that time and it was inspirational.
"It came out of nothing and was a wonderful goal from a great young prospect. He is a good finisher and we've seen it again with that goal."
Despite McLeish's delight at his side's efforts, he expressed disappointment regarding incidents in the lead-up to Stoke's equaliser.
The 53-year-old said: "Jermaine Pennant used his experience to get the free-kick after [Gary] Gardner did not move.
"Then Robert Huth had two hands on James Collins' shoulders which meant he could not get off the ground to defend the cross from the free-kick."
Midfielder Chris Herd had to be sent to hospital following a clash of heads with Huth during the match but the Scot insisted the injury is not cause for concern.
He added: "He felt sick after the game and has gone to hospital for a check-up but wasn't unconscious so hopefully there is no concussion."