The heavy defeat at Tynecastle leaves Killie in 11th place in the Scottish Premiership with two games left to try and save themselves from a relegation playoff.
Johnston was the target of a furious reaction from travelling fans, who held up a banner reading 'AJ Out', and their chants in his direction were branded as 'disgraceful' by Hearts boss Gary Locke.
"To be honest with you, that was embarrassing," Johnston said. "A poor performance. That's as frank as I can be.
"In the position we're in we've got to show more desire. That is unacceptable because our futures are on the line.
"You've got to be worried. If we put performances on like that, we're going to get relegated. It's just not good enough.
"Of course you are going to notice those chants. But you're the manager - you get the praise when it's going well, you get the stick when it's not. Deservedly so this time, because that's not good enough. From everyone."
Locke, who used to play for and coach Kilmarnock, said: "The treatment he got today was a disgrace. It's not for me to tell Kilmarnock what to do, but I know Allan well.
"He's a close friend of mine and a fantastic coach and manager.
"I really hope they get the results they need in the next two games because I spent seven years at the club and it's a great club with great supporters and I certainly wish them all the best."
Locke was also full of praise his side's overall performance, giving the credit to the whole team despite a brilliant display from Ryan Stevenson who scored a first-half hat-trick and set up their other two goals.
He added: "We're delighted with the performance and to score five goals at home. Ryan Stevenson was fantastic, but it would be wrong to single anyone out because we were magnificent as a team, scored some great goals and played some great stuff.
"I'm especially pleased for our supporters because they have backed us all season and that's the type of performance they deserved."