The school's outgoing athletic director, Brian Faison, announced at a news conference later joined by Samuel, that the school would not renew the contracts of Samuel and his staff for next year.
"We've done things that weren't done here before," said Samuel, who also said he was pleased by what his players did.
NMSU has a program "with all the potential in the world," he said.
"Hopefully the next guy gets some of the things that I wanted," Samuel said.
There was widespread speculation that Samuel would be on his way out without a winning season this year, his eighth. The Aggies, who are moving to the Western Athletic Conference from the Sun Belt Conference, finished the year 5-6 and 4-3 in the Sun Belt.
Faison said management issues, academics and the team's competitiveness were all factors in the decision, which he said was reached Tuesday night. Samuel said Faison gave him the news Wednesday morning.
"There wasn't any one factor, there wasn't any one game, there wasn't any one season," Faison said.
The Aggies have not gone to a bowl game since 1960, and only a Sun Belt Conference title would have ended that drought.
Faison said Samuel had done a good job of bringing NMSU's program "to another level," but added: "The reality is we are moving to another level of competition."
"I think you're going to go after a coach that brings strong recruiting to the table," he said.
Samuel was one of five black head coaches in 117 Division I-A schools going into the season. Coach Fitz Hill recently resigned from San Jose State after his fourth straight losing season.
NMSU has had only four winning seasons in the past 35 years, including two during Samuel's tenure. Samuel ranks third in career victories at NMSU with 34.
Faison said NMSU had not contacted any possible successors to Samuel, but "we'll move quickly at this point."
Faison, promoted to assistant vice president for athletic development to help Aggie fund-raising, said NMSU hopes to hire a new athletic director before hiring a new coach. The search for a new athletic director is continuing.
The Aggies' 15 conference wins in the last four seasons are the most for the school since an 11-win run from 1936-38. Two years ago NMSU finished 7-5 -- the most wins in a season since 1967 -- and just missed winning the Sun Belt title.
Faison said the decision not to renew the contracts was not reached easily.
"I think Tony had a chance, I think resources are an issue," he said. "We have got to go out and we've got to do a better job of providing resources for our coaches to compete."
The school wants a coach who is a good recruiter, a good manager and is committed to strong academic performance by the players, Faison said.
Aggie quarterback Buck Pierce, a senior, said the decision was tough to hear.
"You're with them [coaches] through the blood, sweat and tears," he said. "It's a very emotional time for me and a lot of other players."