The 36-year-old millionaire businessman thanked everyone who supported him in the process after failing to secure nominations from county councils which were crucial to his path to enter the campaign.
Having already secured nods from Kerry and Tipperary county councils, he needed just two more local authorities to nominate him to formally enter the race.
However, major setbacks at Meath and Offaly county councils meant his campaign was “mathematically” over.
Mr Sheridan, a married father of an almost three-year-old girl, lost out on a nomination from Meath by just one vote.
Speaking to reporters at Offaly County Council, he said: “We tried to offer something different.
“I think diversity on the ballot is important and we tried to offer that.
“Unfortunately it didn’t work out this tim