He said: "I've made my plan as I think it's very important for the club to know in which direction we will go.
"This not a question for me of money - I know the situation from the club and my person is not important, the important is thing is the club.
"I'll give the board our targets and I hope they accept this; in the transfer window maybe some of our players are very interesting to other people and if this is the case, I have my plan and I know who must be replaced.
"I have never in my life had a problem with owners or directors or boards. I try to bring success to the club.
"We must have a very clear position about what's important for the club, for the players and supporters as you must have satisfied people."
Kilmarnock had dominated attacking play the first half before Eggert Jonsson and Christian Nade netted Hearts' goals in the final quarter.
Tynecastle goalkeeper Janos Balogh saved an 87th-minute penalty from Kevin Kyle, with the hosts' consolation goal coming a minute later from Craig Bryson.
Laszlo called the first 45 minutes "complete s***", and continued: "It was important for us to win this game - it showed that we stay together and we have confidence.
"I care about my players and the club, and today the players definitely gave me something back and I think that relationship is there.
"You have good and bad times in football games, and in the bad times you can recognise who is your friend and who is your enemy."
Lee Wallace was withdrawn at the interval after taking a kick to the ankle, and Laszlo said: "He'll have a scan and it could be one or two weeks. His ankle was swollen but we hope it's nothing, maybe a kick against the bone."
Jim Jefferies was left to rue Kilmarnock's missed opportunities, including one from Frazer Wright just before Hearts opened the scoring at the other end, but praised his side's performance.
The manager said: "We were so far in front until they scored, but you find out sometimes that the game can kick you in the teeth.
"We outplayed Hearts totally up to their first shot on target and then they got a reward from that.
"We should have been at least three in front but then they went from being lucky to be in the game to 1-0, which gives them something to hang on to.
"I wasn't critical of the players afterwards. I said we've outplayed them, you've passed the ball and you've competed well.
"You can't put the ball in the net for them - that's something they've got to do themselves and we created opportunities to do so, but we missed our opportunity to put ourselves in the driving seat."