Jefferies succeeded Csaba Laszlo within two hours of the Hungarian's dismissal on Friday night.
The new Hearts boss lost his first match in charge at St Johnstone on Saturday, but Jonsson believes the squad are more focused for the cup meeting with the Buddies.
The 21-year-old remembers all too well the pain of losing a League Cup semi-final to Rangers just over two years ago and hopes to atone in Lanarkshire.
He said: "Jim knows what the club is all about. He has the 'old school' British attitude if you like and hopefully he will give us all a lift.
"It's a new start for everyone. We start with a clean sheet and we all need to prove to the manager that we are worthy of a place in the team.
"The new manager had little time to prepare for the game on Saturday but tonight is a massive match and we have to make sure we win it.
"If we can do that then we have a cup final to look forward to and that would be a good start for the manager.
"I played in the last semi-final when we lost to Rangers at Hampden a couple of seasons ago.
"We had the chance to get into a final and I don't want to have that feeling again. Hopefully we can make sure we can go all the way.
"It's a new era at the club so hopefully most players will take part in it."
Jonsson admits Laszlo's exit came as a shock, given the fact he took training on Friday and sat with the media for two pre-match press conferences.
He added: "It was a surprise when it happened as we had trained with him on the day, but it's over and done with now and we can't dwell on it.
"I can only speak for myself and I always gave 100% in matches for him. You would have to ask the other players but I don't think I ever let him down."
Jefferies left it late to complete the first signing of his second spell in charge last night, as former St Johnstone attacking midfielder Ryan Stevenson joined from Ayr United.
The 25-year-old, who began his career as a trainee at Chelsea, moved to Tynecastle for an undisclosed fee.
As part of the deal, young left-back Rocky Visconte went in the opposite direction on loan until the end of the season.
Stevenson told his new club's official website: "I never imagined I would be coming here. It's a bit surreal.
"Outside the Old Firm, this is definitely the biggest club so I am over the moon that I am going to be here."
Source: Team Talk