Jack fired home from around the centre spot after St Johnstone goalkeeper Peter Enckelman had fallen short with a clearance to put the Dons two up in the 79th minute. The Scotland Under-21 international had a major part in Scott Vernon's 14th-minute opener when Enckelman could only parry his 20-yard strike.
Brown said: "We have played far better and lost games this season. The fact Ryan Jack did so well to create the first goal and the second was inspirational. It's very difficult to do, score from the halfway line with no goalkeeper. Sometimes we try it in training and it's difficult with no competition, so to do it in the heat of a game is excellent."
Brown felt Andrew Considine was given a harsh second yellow card for a foul on Sam Parkin, although he praised referee Steven McLean for consulting with both clubs before allowing the game to go ahead in heavy rain and strong winds.
"I have seen it on television and it was a cleanly-won challenge from Andrew Considine," said Brown, who lost Youl Mawene to a knee injury.
"We lose Andy for Saturday's match, very, very unfortunately and unfairly. It's a very, very cruel decision from a very good referee."
St Johnstone manager Steve Lomas refused to blame the conditions or Enckelman.
Lomas said: "Obviously he is disappointed. He is a senior pro, he has held his hands up, but I have said to him 'we win as a team and we lose as a team'. It's unfortunate, it's slippy conditions and credit to the lad for finishing it. But it's not Peter Enckelman's fault that we lost the game."
The Northern Irishman added: "There are no excuses. It was difficult conditions but it's the same for both sides."
Source: PA
Source: PA