The 24-year-old Scotland defender - whose Bairns deal expires in the summer - had also been courted by Hibs, the Dons, Dundee and more than one club in England.
Laszlo believes Barr has paid attention to how Hearts nurtured the likes of Christophe Berra, Robbie Neilson, Christos Karipidis, Deividas Cesnauskis and Saulius Mikoliunas, all of whom went on to secure moves elsewhere last season.
"We brought many, many players out who have gone on to a higher level," Laszlo said.
"A lot of players who last season left the club found - I don't like to say a better club - but a club they think was good for them."
He added: "The highest level was reached by Christophe Berra, being not just part of the national team (squad), but being on the field.
"Mike Stewart, from his performance, I think is in the (attentions) of the national coach.
"Andrew Driver, (England) Under-21 - don't forget this.
"I think the young players who come to Hearts know, 'This is a big place for me to achieve something'."
As well as being a fan of Barr the player, Laszlo is also a huge admirer of Barr the personality, revealing the defender could be a future captain at Tynecastle.
"A leader is always a leader," he said.
"I don't see any problem in taking a player who was not here before and making him captain.
"If I feel he has this ability, I can't ignore this."
Hearts were today fined £10,000 by the Scottish Football Association for failing to clean up their act this season.
Laszlo's side have seen red eight times since August and he was fuming on Saturday when Christian Nade got himself sent off in the 1-1 Scottish Premier League draw at Rangers.
Hearts have complained in the past of a witch hunt against them but Laszlo rubbished this, saying: "This is stupid. We punished ourselves.
"We have a problem paying the money - the club have a problem.
"I am definitely, definitely very angry about this."
There have been reports Laszlo had lost patience with Nade and the striker would not be offered a new contract.
The Hearts boss, who will discipline the Frenchman, insisted that would be going too far.
But he reiterated his plea for a new striker before the transfer window closes, claiming competition for places would make Nade think twice about keeping his discipline in future.
He said: "If you have competition, you know for the next mistake, another player has a good game and for the next five games you sit just on the bench."
One player who vowed to clean up his act today was midfielder Ruben Palazuelos, who returns from suspension for tomorrow's clash with Aberdeen.
The Spaniard was sent off in the Edinburgh derby earlier this month for headbutting Darren McCormack.
But despite admitting being in the wrong, he suggested Hibs boss John Hughes had also tried to provoke him as he left the field.
"I read something after the Hibs game about John Hughes saying he told me, 'Calm down'," Palazuelos said.
"It's not true."
Source: Team Talk
Source: Team Talk