The 25-year-old was brought to Edinburgh by Laszlo last summer and started the opening Scottish Premier League game of the season at Dundee United.
But he made only a handful of appearances after that and suffered the ultimate indignity of being substituted 28 minutes into December's 2-1 defeat at Hamilton.
Jefferies' arrival and a defensive injury crisis gave Kucharski another chance, something which has boosted his self-esteem immeasurably.
"The manager trusts me much more," said Kucharski, who admitted Laszlo did not feel that way about him.
"I feel when I do something wrong in the game, in training, he doesn't punish me.
"He doesn't say, 'You're a bad player' or something like that.
"He says something good: 'Next time you'll play better'."
Of all those in the Hearts squad, it appears few were more pleased to see the back of the colourful Laszlo than Kucharski.
"I feel better, much better," he said.
"I try in the training and in the game to watch the manager.
"I feel very, very good now and I feel stronger."
Kucharski still smarts from the humiliation of his early substitution at New Douglas Park and revealed he used that as motivation when Accies came to Tynecastle on Sunday.
"I don't know why the coach took me off," he said.
"But in the last game, Hamilton at home, I remembered that game and I tried to show I'm a good player.
"We won 2-0 and I showed what I could do."
During his post-match interview defeat after December's defeat at Hamilton, Laszlo laid the blame squarely at Kucharski's feet for the loss of two early goals.
"He didn't say anything to me," the defender said.
"Afterwards, when I watched the game on video and analysed this game, I didn't know why he took me off."
In fairness to Laszlo, Kucharski was all at sea during that game but it appears his problems under the old regime may have stemmed from being played out of position at right-back.
"I prefer being in the middle," said Kucharski, who joined Hearts from Lech Poznan.
"In my last team, I played only sometimes at right-back.
"But my position is centre-back."
Jose Goncalves' refusal to sign a new contract and an injury to Ismael Bouzid handed Kucharski the chance to partner Marius Zaliukas in recent weeks.
"When we play together, I listen all the time to what he says to me," Kucharski said of Hearts' vice-captain.
"He tries to help me and this is very good for me."
With Bouzid close to returning, Kucharski will need to improve further to keep his place.
He believes cementing the Jambos' top-six status with victory at Aberdeen tomorrow can help him achieve this.
He added: "This is very important for us. We don't have anything (else); we don't play in the cup.
"We must fight for the top six and a good position at the end of the season."
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Source: Team Talk