Replays suggested Olsson was already going to ground before any contact was made and Laws said : "When you look at it in the cool light of day it's clear it's not even a penalty.
"Olsson's took a dive, he's conned the referee. The referee's not in a great position and he's given the penalty which was very harsh and left us with a mountain to climb.
"But we didn't get a lot of joy from any of the decisions today and I was disappointed with that. I thought it might even itself out.
"If the referee thought it was a penalty by the goalkeeper then you either send him off or book him.
"I'm not blaming the player, he's done everything possible to try and get a goal against us through a penalty or his own work, but I'm disappointed because we want to see honesty and we want to see the referee get the correct decisions."
Rovers boss Sam Allardyce admitted his side had been fortunate to be awarded the penalty.
"It's slightly harsh against Burnley when you look at it from the angles and you slow it down," Allardyce said.
"But when you look at it from Mike Dean's position and his point of view it definitely looks like a penalty.
"I was jumping up and down like a lunatic when he was brought down, so for me it looked like a penalty.
"There might only be slight contact, but there it's gone for you rather than against you.
"In a big game like this you need a little bit of luck and perhaps we have had that."
Dean was at the centre of controversy again with around 15 minutes to go after he failed to spot a clear handball by Rovers goalkeeper Jason Brown as he fumbled the ball outside his area.
To the dismay of the vociferous home crowd, Dean waved for play to continue and Laws felt the official's decision-making began to have an impact on his players' concentration.
"The goalkeeper has gone out of his box and you can see quite clearly that he has handled it. Yet, he (Dean) just played on," Laws said.
"It does wind the players up because it frustrates them and they end up arguing over it for a few minutes rather than getting on with the game.
"It's just very disappointing that we didn't get any fairness within the game."
Dunn's strike - his third of the week after a match-winning brace against Birmingham on Wednesday - eventually proved the difference in the first top-flight meeting between the two sides at Turf Moor since the 1965-66 season.
The result moved Blackburn up to 10th and increased Burnley's relegation fears, leaving them three points adrift in the drop zone with six games to play.
"Everybody will write us off and say that we're down, gone, that's it, we're finished," Laws said.
"Maybe even our own supporters might be feeling like that. But the facts are that it is still mathematically possible, so while that is still in our hands we will keep believing that we can do it and we need the supporters to support the players so they can maybe achieve it.
"We are going to have to get three, maybe four wins, no matter whether we get it at the beginning of the six games (left) or at the end. But the one thing is that we won't give up."