DeAngelo Hall, who spent the past four and a half seasons with the Redskins, was released Monday as the team tried to create space under the salary cap. (Jonathan Newton/THE WASHINGTON POST)

Forced to make moves to get below the NFL-mandated salary cap of $123 million, the Washington Redskins released cornerback DeAngelo Hall, restructured defensive end Adam Carriker’s deal and were in the process of negotiating several other contract revisions.

The team has to be under the cap by 4 p.m. Tuesday, which marks the start of the new league year and free agency. Washington entered this past weekend roughly $3 million over the cap but still re-signed starting left guard Kory Lichtensteiger (an impending unrestricted free agent) and four restricted free agents: tight end Logan Paulsen, fullback Darrel Young, linebacker Rob Jackson and long-snapper Nick Sundberg. They also extended a right-of-first-refusal qualifying offer to backup nose tackle Chris Baker.

Those moves put the Redskins further over the cap. But the release of Hall saved the team $8 million, and the reworking of Carriker’s contract is believed to have saved another $2.6 million. As of Monday evening, Washington sat at “about a million under the cap,” Coach Mike Shanahan said. “But if we do make some moves, some people will have to be released,” he added.

Shanahan described the decision to release Hall — a 10-year veteran, who had spent the last 41 / 2 seasons in Washington — as difficult. He reiterated that Washington found itself in the salary-cap predicament because of the $36 million penalty the league leveled against the Redskins last year for the way they restrucutured some contracts during the uncapped 2012 season.

Hall has “given everything I’ve asked him to give,” Shanahan said. “He’s gotten better each year, and when you have to tell somebody that they’re not going to be on your football team, it’s hard, especially when your plan was to take care of the guys that took care of you. . . . So, it’s pretty tough on me when I’ve got to tell some of these players over the next month or two, or could be days or weeks, depending on what direction we go or how it’s done, that we have to make these cuts, and the reasons, it’s very tough for me to share with them. But anyway, we’ve got to make these cuts, as I told D-Hall, and he was quite graceful.”

Reached by phone, Hall said he knew why the Redskins had released him.

“I understand the business side of things,” Hall said. “I thanked him for the opportunity and wished them luck. Mike said he really felt bad because I had done everything they asked. . . . I just wish it had happened sooner than later. But it came down the wire. But Mike did reach out to me.”

Hall’s representatives had proposed a contract restructure in recent weeks because it was his desire to remain in Washington. But the Redskins opted instead to cut ties with him and, in Shanahan’s words, to give Hall the chance to earn more money elsewhere.

Carriker, meantime, said “I’m glad to help the team with the salary-cap issue,” particularly compared to the alternative of being released. Carriker, who re-signed with Washington last season for a four-year deal, was set to count $4.75 million against the cap. But early in the second game of the 2012 season, he tore his right quadriceps and missed the rest of the year. In his absence, second-year pro Jarvis Jenkins took over as starter. So the Redskins could have been inclined to part ways with Carriker for a cheaper alternative.

Instead, Washington lowered Carriker’s cap number for the 2013 season, but the team did not extend his contract.

Meantime, the Redskins have more work to do to create flexibility beneath the cap so they can re-sign more free agents of their own and add talent through free agency.

Veteran wide receiver Santana Moss will count $6.1 million against cap and is a prime candidate to have his contract restructured. But Shanahan said, “no, not at this time,” when asked if Washington was trying to rework Moss’s deal.

It wasn’t immediately clear what other players Washington would pitch restructuring to.

“It’s a case-by-case basis. They have to do what’s best for them, and I understand that,” Shanahan said. “We’ve got some guys that I feel very fond of, and if they’d like to do it, I’d love to have them back, but if not, I understand their situations as well.”

The team still hopes to re-sign linebacker/special teams captain Lorenzo Alexander and tight end Fred Davis, who become unrestricted free agents Tuesday.

Cornerback, safety and right tackle also remain key needs for the Redskins. The team had expressed interest in free agent cornerbacks Greg Toler and Derek Cox, and right tackle Ryan Harris also was believed to be on Washington’s radar. But the team also could turn to April’s draft to meet those needs.

Note: Shanahan says quarterback Robert Griffin III is working out at Redskins Park twice a day for a combined six to seven hours to rehabilitate his injured right knee. The coach says he has “no idea” if Griffin will be ready for Week 1 of the regular season, but adds, “If work has anything to do with it, he probably will.”