Jonevret's side managed to shine some light on an otherwise dull 80th-anniversary campaign as they advanced to the Ke Yona quarter-finals after thrashing Ea Lla Koto 4-1 at James Motlatsi Stadium in Orkney.
Pirates' overall form this season, though, has caused much agony for the Ghost, with even a top-eight finish in the Absa Premiership looking unlikely with only eight games to go.
But with Mamelodi Sundowns having bowed out of the Nedbank Cup after a defeat to Golden Arrows, joining the likes of Cape Town City and Ajax Cape Town in early exits, Jonevret sees a chance for the Soweto giants to rescue something this season.
When asked if he liked their chances of challenging for the crown, Jonevret said: ”Yes, but at the same time the cup is the cup and big teams crashed out and Sundowns, the two Cape Town teams are out.”
The likes of Kaizer Chiefs, SuperSport United and Bloemfontein Celtic are also into the quarter-final draw, and while Jonevret admits it will not be all smooth sailing, he remains confident of his side’s chances.
"It'll depend on the draw, of course, but I mean we have an absolutely big chance to win it following [the exits of] those teams I've mentioned. We are still in the cup and that is important and it's always tough,” he added.
"But the cup is the cup and it's always tough and if we can play like this [against Free State Stars] at least other teams have to be good to beat us."
The former Djurgadens IF coach says he never envisaged his side would score four goals against Stars, having lost to the same opposition in last week's league match. But he felt positive about a win even before the kick-off, given the players’ attitude leading up to the game.
"You can never expect four goals but I thought what I saw in the eyes of the guys after last game, they were not satisfied after we lost last Saturday," he said.
"We had a good training week and the feeling in the locker room was 'we should stay in the cup, we should stay in the cup' but you never expect four goals."
Jonevret's side, whose last trophy came via the same competition in 2014, will learn the identity of their quarter-final opponents in tonight's draw, where Pirates are in the hat along with Chiefs, SuperSport, Arrows, Chippa United, Celtic, Jomo Cosmos and Platinum Stars.