Ghana midfielder Kingston, 29, was handed his first appearance for more than two months by Jefferies when he came off the bench in Sunday's 2-0 Scottish Premier League win over Hamilton.
He took to the field to a mixture of cheers and jeers from the home fans, who Jefferies has urged to give Kingston the benefit of the doubt.
The playmaker is determined to repay Jefferies' faith in him, telling Hearts.TV: "It has been a long time since I last played and I was happy to see myself back at Tynecastle. It was great to be back.
"No-one is perfect and everyone has problems in their career but I just want to get back playing.
"I am so, so happy about the new manager. He is like a father to me now. The first time I met him, I was so happy with the way he spoke to me.
"He is an experienced manager and, the way he spoke, I knew he has something to give this club.
"Everybody is happy in training and the morale in the dressing room has changed. It is a very good thing he is here.
"It is important that I don't let him down as he has supported me so well. I know I have to work hard in training and in games.
"It is not about me talking, I have to stay quiet and deliver on the pitch, give 100%."
Meanwhile, fellow midfielder Eggert Jonsson will miss Hearts' trip to Dundee United on Saturday week after his yellow card on Sunday triggered a one-match ban.
Aberdeen Evens, Draw 12/5, Hearts 11/4
Source: Team Talk