"It just didn't seem to be in keeping with our long-term plan," Johnson told reporters at the NFL owners meetings in Orlando, Florida.
The Jets' interest in Suh, which surfaced on Friday, came as a surprise. That they've pulled the offer also is a surprise.
The Jets made a "pretty big offer" to the former All-Pro, Johnson said. Suh told Yahoo! Sports that it was the largest offer he had received since he was released by the Miami Dolphins. He's also drawing interest from the Los Angeles Rams, Tennessee Titans and New Orleans Saints.
Johnson said the Jets decided to change course after he discussed the matter with general manager Mike Maccagnan. Coach Todd Bowles wasn't part of that conversation, according to Johnson, who wasn't involved in the decision to make the initial offer.
"I had a lot of discussion with Mike about this," Johnson said. "Our thinking just changed. That's where I have to leave it."
He declined to elaborate.
Maccagnan, speaking to reporters on Monday, said their offer to Suh came with a deadline.
"The deadline passed, and we had to make a decision on if we wanted to stay in or stay out, and we decided to move on," said Maccagnan, adding that Bowles was kept apprised of the developments.
Maccagnan described Suh as "a very good player, not from a statistical standpoint, but when you watch him on tape, he still has the ability to be a dominant player. We felt pretty good about potentially adding him to the roster."
The Jets are looking to replace defensive end Muhammad Wilkerson, who was released because of salary-cap and production concerns. Bowles, who has spoken glowingly of Suh in the past, reached out to him with a recruiting pitch, explaining that they could use him in their defense.
The staff felt that Suh, 31, could be a valuable addition, a disruptive player who could draw extra blockers. Johnson himself described Suh as "one of the best football players out there," but he evidently didn't want him on his team.
Johnson didn't want it to be characterized that he interceded, saying it was a joint decision with Maccagnan.
"It became apparent to the two of us that this just didn't work," Johnson said.
The Jets still have more than $30 million in cap room. They've been emphasizing youth during free agency, and Suh's age likely was a turnoff. Suh also has a reputation for not being a team player.
"I don't want to be a flash in the pan," Johnson said, speaking of his team-building approach. "I don't want to load up on people who can get you there but can't keep you there. This is about building something great long term."
In other developments, Johnson said he was "absolutely" disappointed that quarterback Kirk Cousins didn't take his team's free-agent offer, but he expressed optimism about the Jets' "Plan B" at quarterback. The Jets traded up in the draft, from No. 6 to No. 3, presumably to take a quarterback.
"It's almost a shame to call it Plan B because it's shaping up as something pretty magnificent," he said. "I'm really excited about it. ... It doesn't hurt at all that we have an awful lot of money that we might have been sending out the door to one player now back with us."
ESPN's Kevin Seifert contributed to this report.