[1][5][6][8] Ștefan Kovács started coaching in 1952 at Universitatea Cluj while also being an active player, helping the club finish the season on the fifth place.

[10][12] Kovács came back at the club for a third time for the first half of the 1956 season, being replaced with Nicolae Munteanu for the second one, the team relegating to the second league at the end of it.

[5][6][7][8] At the beginning, the stars of the team were skeptical of him leading them, Johan Cruyff at one point shot a ball towards the edge of the field where Kovács was talking to one of the assistants, intending to hit him but he saw the gesture with the corner of his eye, so he quickly turned around and made an impeccable stop, after which he returned the ball to Cruyff, saying:"Use the inside more when shooting".

[5][6][7] In his first season he won the league title, the KNVB Cup after a 3–2 win over FC Den Haag in the final and he won the 1971–72 European Cup, getting past Dynamo Dresden, Marseille, Arsenal and Benfica in the campaign, then defeating with 2–0 Inter Milan in the final, courtesy of a brace scored by Johan Cruyff.

[5] During his spell at Ajax he was known for promoting a more relaxed environment in the team, Johann Cruyff saying:"Ștefan Kovács was a very pleasant coach, but much less strict than Michels when it came to discipline.

[5][6][8][10][21][22] In this position he raised the young generations of French talents, giving the debut to 33 players, including Dominique Rocheteau, Bernard Lacombe and Alain Giresse.

[5][9][24][26][27] He then guided the national team in three games at the Euro 1980 qualifiers, being replaced in late 1979 by his assistant Constantin Cernăianu but remaining as the technical director of the squad.

[5][6][7][8][10] He wrote one volume about football:[6] When talking abouth his ethnic origins, he said he is:"Romanian by mother, Hungarian by father, Jewish by grandparents and a little Serbian by great-grandparents".