The 2-1 loss to Abafana Bes'thende saw Bucs finish outside the top eight on the league standings for the first time since the inception of the PSL in 1996.
“There’s no other way, we need to apologise to the fans for the disappointing season we had," Jonevret told Daily Sun.
Pirates goalkeeper Jackson Mabokgwane was at fault for Arrows' first goal, while the Bucs defence was caught napping in stoppage-time and Knox Mutizwa netted Abafana'Bes'thende's winning goal
"The only way to do so is by winning the Nedbank Cup final, it’s as simple as that," he continued.
“I’m both angry and disappointed. After scoring first and taking that lead into the break, I told my players at half-time to put more pressure on Arrows.
"I told them to play high balls to (Thamsanqa) Gabuza and (Tendai) Ndoro. But what they did was the absolute opposite, allowing them to come at us," Jonevret added.
“I thought we had an understanding – we’ve been solid in defence in a couple of matches. I’m really angry at the way we played today.
“My disappointment has nothing to do with our league standing. I’m disappointed because I really wanted to win this last match," he added.
The Buccaneers will now take on SuperSport United in the Nedbank Cup final at the Moses Mabhida Stadium on the 24th of June 2017.
"I wanted to beat Arrows twice in a row – and it’s not like they were better than us. We gave them this win and I hate it," the Swedish stressed.
“I have requested two tough opponents to prepare for the Nedbank Cup final. I hope we get these friendly matches because I want us to be better prepared for the final.
"This cup is not important to me, this is for the team and supporters,” Jonevret concluded.