Pirates advanced courtesy of Thamsanqa Gabuza's 103rd-minute winner in Soweto after Celtic's Kabelo Mahlasela struck late in regulation time to cancel out Abbubaker Mobara's 54th-minute opener.
The Sea Robbers are in tonight's last-four draw in Randburg alongside cup holders SuperSport United, Chippa United and Golden Arrows.
"I think they wanted so much to win this one and I think they were a little bit nervous. But I mean staying in the cup right now is important," said Jonevret.
"But I was not happy the way we played after we have scored two times. But in the end we are happy of course because we are in the hat for the draw."
Meanwhile, the Swede is well aware his team have a fight on their hands to preserve their PSL record of always finishing in the top eight in the league since 1996.
Pirates are ninth on the table with 27 points from 23 matches - two points behind eighth-placed Maritzburg United, and four shy of Golden Arrows and Polokwane City.
However, Bucs can draw encouragement from having a game in hand on the three teams directly ahead of them as they prepare to host bottom club Baroka at Orlando Stadium on Wednesday night.
"It's going to be a hard race because you can see it's not a big difference to the top clubs to the club in the bottom in the last six/seven games," said Jonevret.
"All the teams down there have to get the points to be not relegated. So it's going to be tough and I'm a 100 percent sure about that.
"It's not easy to beat Highlands and SuperSport for example and we know that it's going to be tough. Even if we have a tight schedule of course, it's going to be tough. But nights like this can give us confidence because there's a lot of football [to play] but we've to keep on working."