Speaking to MLB.com on Saturday, Sosnick insisted there are no hard feelings, and both sides now are prepared to move forward on a one-year contract for 2010 because this is Johnson's second season eligible for arbitration.
"We talked twice for a total of 30 minutes," Sosnick said. "Everything happened this week. There were no hard feelings about it, no harsh words. They offered us a deal that we felt was way under market value for the dollars and years."
Per team policy, the Marlins do not speak publicly on contract negotiations.
Sosnick said after the initial conversation reached a stalemate, he made a follow-up phone call.
"I called again and said, 'Are you set? Is there not going to be a fourth year guaranteed?'" Sosnick said. "They said, 'There is not going to be a fourth year guaranteed.'"
At that point, the two sides said they would get in touch at a later date to work out a one-year contract for 2010.
Johnson, 25, had a breakout 2009 campaign, finishing 15-5 with a 3.23 ERA. He logged a career-high 33 starts and 209 innings.
With a $36 million payroll, the Marlins finished with 87 wins and in second place behind the Phillies in the National League East.
Florida's payroll in 2010 is expected to be about $36 million, or slightly less.
Without getting into specific dollar figures, Sosnick said the Marlins offered three years with a club option for a fourth.
Johnson's camp was hoping the deal would at least match what Kansas City's Zack Greinke signed before the 2009 season. The Royals' ace, recently named the American League Cy Young Award winner, signed for four years at $38 million.
In his first year of salary arbitration, Johnson made $1.4 million, plus another $50,000 in bonuses. The 6-foot-7 right-hander was selected to his first All-Star Game, and Sosnick said: "Outside of [Tim] Lincecum, J.J.'s probably the next-best young pitcher in baseball. So given that, what kind of player are you looking to build your team around?"
Lincecum, the Giants' two-time Cy Young Award-winning right-hander, also is 25 years old.
Johnson remains under Marlins control through 2011, before he is eligible for free agency for the 2012 season.
A four-year deal would have closed out Johnson's final two seasons of arbitration, plus two potential years of free agency.
Sosnick has held a hard stance that for Johnson to sign a multiyear contract with the Marlins, he would have to do so before the 2010 season.
Asked on Saturday if talks for a multiyear deal could pick up again once both sides had time to reconsider, Sosnick said: "No. I don't see it changing. We're to the point right now where I've kind of moved on. If Josh signed a four-year deal with them, we'd be giving up a tremendous amount of money in two free-agent years. We would have done it anyway, because Josh really wanted to stay in Florida. We told them that. The fact they were not interested made a tough choice much easier. It probably saves Josh $10 million."
Sosnick feels 2010 will be Johnson's last with the Marlins, if the team wants to maximize his trade value. Since the Marlins aren't revealing their intentions, that is purely speculation.
In the past, the Marlins retained pitchers A.J. Burnett and Carl Pavano in their final arbitration years, and then received Draft pick compensation when both opted for free agency. On the flip side, Josh Beckett, Dontrelle Willis and Miguel Cabrera were dealt before their final years of arbitration.
"We disagreed on the years, which is fair," Sosnick said. "As far as our feelings are concerned, and I feel very strongly that this is true, that Josh either signs a long-term deal now with the Marlins, which is not going to happen, or he gets traded after this year and the Marlins can get some value back.
"Whoever he gets traded to will probably ask for a long-term deal for the Marlins to get what they're asking for him. So to me, Josh either signs a big contract this year, or a big contract next year. If the absolute worst-case scenario occurs and the Marlins decide to keep him for two years, and get Draft picks in return for him, which I don't see happening, then [free agency] is two years from now."
Sosnick said he doesn't see any problem working out a one-year contract for Johnson in 2010, and he stated his respect for the Marlins' front office.
Derek Jackson, the team's vice president and general counsel, puts together the Marlins' arbitration cases.
"The guys that do the arbitration for the Marlins, guys like Derek Jackson, they are incredibly smart guys, particularly Jackson," Sosnick said. "Those guys evaluate and have a pretty good understanding of the arbitration process."
Sosnick added that for the resources the Marlins have, president of baseball operations Larry Beinfest and general manager Mike Hill rank among the best in the game. With less, the Marlins have shown they can field competitive clubs.
"The strategy the Marlins have used has been good for the Marlins," Sosnick said. "They've been competitive almost every year with less. You're going to have a very hard time convincing me that Beinfest and Hill aren't the most effective GMs in the league.
"I'm disappointed that we didn't get a deal done. But look at their track record. Think what those guys could do if they had $200 million, or $150 million in salary, or $120 million in salary. Think about it. They're unbelievable the way they've managed the team. I can't begrudge the choices they make, because the choices they make generally are very good."