Bayern climbed to second in the Bundesliga, nine points behind leaders Borussia Dortmund, after Robert Lewandowski netted twice before Franck Ribery added a third at the Allianz Arena to give Kovac's side their third straight win in all competitions.
The defending champions seem to have turned the corner after a poor run of form -- including a 3-2 defeat at Dortmund last month -- had left Kovac's position uncertain.
"If you win, especially here at FC Bayern, then you get some peace," said Kovac, who now has some breathing space after his side's mini winning streak.
"I've been here for five months now, in that time I have seen a lot of things, gained a lot of experience.
"I am trying to put that to good use and to improve."
Having announced on Friday that he is ditching squad rotation and from now on will only change his team for injuries or suspensions, Kovac was pleased to see his team keep its first clean sheet in the league since September 22.
"We didn't let anything get through (our defence) over the 90 minutes and hit the woodwork twice," said the 47-year-old.
"I am happy we have finally kept our opponent goalless, not given away a goal or lost our shape after conceding one."
A fourth win in a row on Wednesday at Ajax will see Bayern win their Champions League group having already reached the last 16.
He will be boosted by Thiago Alcantara and Kingsley Coman playing the last 27 minutes on Saturday to build fitness after coming back from injury.
Germany centre-back Mats Hummels was the most noticeable big-name left on Bayern's bench and Kovac explained before kick-off why he is ditching rotation, risking unrest in a squad packed with star names.
"I've done it because we won the last two games and also played well, not only going forwards," said Kovac.
"The rhythm is there, the boys are in the flow, therefore we didn't want to change anything."