Bucs progressed after winning 3-1 at Sisa Dukashe Stadium, with goals from Dove Wome, Mpho Makola and Thamsanqa Gabuza sealing the result after Bees had threatened to rally when Bongani Chilika had made it 2-1.
However, it was still far from a complete display in the opinion of the Swedish coach, although he was still able to take plenty of positives after Pirates snapped their 12-game winless streak.
"They were good and had lot of energy, but we had some problems with our passing game and we lost a lot of balls," said Jonevret after the game.
"But this team has a lot of talented players but right now they are a lot less of confident. I think you can see when they are playing, but hopefully there's going to be relief for us.
"I think we had good control of the first half and there were chances but after we had scored the second one, I mean that goal [scored by Bees] should be dealt with by us.
"We should never have allowed them to that one-against-one but you saw what happened, we gave them a goal, a pretty simple one again."
With Cape Town City and Ajax Cape Town both suffering shock defeats to lower league sides in their respective last-32 ties, Jonevret is delighted Pirates are still in the competition and feels a deep cup run may restore confidence in his team after a tough start to the season.
"I'm very happy that we won this one and this [a deep cup run] could help us," added Jonevret, whose side are only next in Absa Premiership action on April 1, away to Free State Stars.
"Now we have three weeks to train and we’ve got no games next week so we have to wait until the beginning of April with another league game.
"Hopefully we can train a bit in the next few weeks and we are still in that [process of understanding each other], we are still there, we are still in the cup.
"Ajax Cape Town, Cape Town City, those teams lost so things happened and this is a tough game."
The draw for the Nedbank Cup Last-16 will be conducted on Thursday at Randburg, Johannesburg, where Pirates will learn the identity of their next cup opponents.