The abrasive Aussie No 8 was outstanding in the 33-14 win over Dragons on Saturday as Wilson’s side returned to winning ways in the United Rugby Championship at Scotstoun.
Attention now turns to the Heineken Champions Cup, with Glasgow travelling to La Rochelle on Sunday followed by a home game against Exeter Chiefs six days later.
It's a mouthwatering double header and Wilson knows Warriors will need to produce something very special in France against last season’s finalists.
“The bar goes up now, doesn’t it?” said the coach. “We’ve looked at La Rochelle over the past couple of days. They are some team, with some star-studded individuals.
“Physically they are huge right throughout their team and there is a lot of power in there.
“So we need to match that and play a style of rugby that’s going to suit playing against the big teams.”
Dempsey will be key to Glasgow’s hopes of pulling off a shock in France and emulating the Warriors side of 2019 who won memorably 27-24 in La Rochelle. He was by no means the only star performer against Dragons - Ali Price, Sione Tuipulotu, Ross Thompson and debutant Josh McKay all impressed in a solid win - but Dempsey’s dynamism in defence and attack was key.
“I thought he was outstanding,” said Wilson. “He’s been outstanding pretty much from the moment he arrived here.
“He’s exactly what we hoped he would be. What we signed was a powerful animal on both sides of the ball, with real rugby nous as well.
“This was probably the best of those performances he’s put in for us so far. I’m really pleased for him and he’s a good example for the standard we want to be at.”
The 14-times capped Wallabies international arrived at Scotstoun in the summer from the Waratahs and his influence has rubbed off on the rest of the squad.
“He’s got plenty of edge,” added Wilson. “He only knows one gear. Even in contact in training, it’s all or nothing with Jack. I like that about him. He’s raised the standards in training.”
Dempsey scored the third of Glasgow’s five tries on Saturday, peeling off the back of a scrum and powering over from the Dragons 22. The other scores came from Sione Tuipulotu and Kyle Steyn in the first half and Price and Johnny Matthews in the second.
Two Dragons tries in the final quarter - from Ellis Shipp and Mesake Doge - flattered the visitors and Wilson was happy with the win, if slightly concerned by the number of turnovers the Warriors conceded.
“There were a lot of positives for us,” he said. “But I also think there are still a lot of things to improve on moving forward.
“If I’m brutally honest I think there is a lot more to come from us because we were a little bit inaccurate at times.
“I think we had 17 turnovers which is way too high, so we have to improve that when we go to La Rochelle next week, and when Exeter Chiefs come here the week after that.”