He is the 2nd most successful Manager in Romania, tied with Dan Petrescu, winning the Romanian First League on 6 occasions, all with Steaua București.

As a child, he moved with his family to Losonc (now Lučenec, Slovakia), because his father did not want to serve in the Romanian army.

In 1978–79, Jenei coached FC Bihor of Oradea, but the team finished the season in last place and he was sacked as a result.

[7] In 1985, he won a new championship and in the following season led Steaua București to victory in the European Cup final against FC Barcelona in May 1986.

In the summer of 1986, Jenei was named co-head coach of the Romania national football team, together with Mircea Lucescu, making his debut against Norway.

Between August 1986 and June 1990, Jenei coached the team in 40 games, including two wins against Spain in 1987 and Italy in 1989.

After the World Cup, He returned to Steaua București in April 1991, for the fourth time, only to be sacked again in December of same year.

He was named head coach of Hungary between 1992 and 1993, but failed to produce notable results, instead he won the Kirin Cup in 1993, an international tournament organized by Japan, and later being replaced by Ferenc Puskás.

Until her death in 2021, Jenei was married to Ileana, former fencer for Romania, world champion and Olympic medalist.