Veteran goalkeeper Marek Stech was also shown the door when the club announced its retained list last week.
“It's always difficult to release players, but we had to make a decision and release a couple,” said Clough.
“We were signing another goalkeeper to replace Marek, but Faz Rawson was a very difficult one as he'd had a good couple of years here.
“It's just with the number of defenders we've got really. With (John-Joe) O'Toole, (Oli) Hawkins, (James) Perch and (Elliott) Hewitt we've got quite a few central defenders and we will probably sign one in the summer as well.
“So, unfortunately, Faz just becomes surplus to requirements.
“But it's been a pleasure having him around and working with him for a couple of years. He is one of the most genuine and honest lads you could ever wish to work with.”
Rawson, signed from Forest Green Rovers, lost his place in the centre of defence in the season run-in and did not even make the bench at Wembley last weekend.
He tweeted: “@mansfieldtownfc it’s been a pleasure! Wishing you nothing but success and happiness for the future.”
Johnson arrived as Leyton Orient's top scorer in a blaze of publicity last summer with a vow to repeat his scoring feats from the East London club.
“It has just not quite worked out with Danny. With all the will in the world sometimes it just doesn't,” said Clough.
“I think it was the timing of his injury.
“Just when it looked like he was going to hit a bit of form, scoring the hat-trick against Newcastle, he was then out for 10 weeks when the fortunes of the team turned around.
“Jordan (Bowery) scored goals, Oatesy (Rhys Oates) scored goals, so it's been difficult for us to be able to give him that opportunity and that run of games that he probably needed.
“So it's just circumstances more than anything, rather than him sitting around again for another season. It is an opportunity for Danny to go and get fixed up.”