North Antrim DUP MLA Mr Storey lost out to Alliance candidate Patricia O’Lynn in North Antrim, while Mr Beggs of the UUP was also a victim of an increased Alliance vote in East Antrim.
Both were long-standing assemblymen, with Mr Beggs having held a seat at Stormont since 1998.
As the results for North Antrim were announced, a former UTV political editor described the Alliance gain as “amazing”.
Ken Reid tweeted: “The most amazing result of the Assembly is here in North Antrim. Alliance’s @PatriciaOLynn taking a seat from the DUP’s Mervyn Storey.”
Mr Storey polled 500 more first preference votes (6,747) than his running mate Paul Frew, however, he did not fare so well from transfer votes and was ultimately eliminated from the contest.
Ms O’Lynn polled 4,810 votes but attracted a large number of transfers to edge out Mr Storey.
The DUP man, who had been an MLA for 18 years, spoke to the News Letter on Sunday and said he was looking forward to the next chapter of his life.
“The thing that has stayed by me, and I have quoted it numerous times over the last couple of weeks, is Romans 8 v 28. For me my faith is central to who I am, and all things work together for good,” he said.
“I have said during this campaign that I wanted [God’s] will and, if that is God’s will at this time in my life then I have got to submit myself to it.
“I’m disappointed first and foremost for my staff because there is the uncertainty of what they face. I have been in politics for 18 years, and I’m 58, so there is another door opening up.
“My staff have given me unstinting service – who have helped me and helped so many thousands of people over the years.”
Mr Storey has served as both the minister for social development and finance at Stormont and was a member of the NI Policing Board for a number of years.
Asked if he will now bow out of elected politics, Mr Storey said: “I just don’t know. I’m not going to make any rash moves.
“My concentration over the few weeks will be how we deal with the run down. You have three months I understand in terms of the office, so we have all of that to sort out.
“There is still a backlog of constituency work that we were dealing with, things that are important to those people, so we have all of that to deal with. The door is not closing tomorrow.”
Mr Storey said there is still “a job of work to be done over the next few months,” but is looking forward to seeing more of his two grandchildren.
Commenting on the wider political situation, Mr Storey said: “The party has a huge responsibility, and a huge job of work to do and, more importantly, unionism needs to take a very, very long look at itself, because you have seen a toxic brand of unionism that has delivered nothing but division within unionism.
“That has to come to an end or else there will be no political unionism in the future.”
In East Antrim, the UUP’s Roy Beggs had been re-elected five times since he first entered Stormont in 1998, however it was clear from the early stages of the count that he was not polling well.
In a brief social media message on Saturday Mr Beggs, who was one of the UUP’s more conservative figures, responded to one well-wisher saying: “Many thanks for your kind words. Politics is a rough game but other doors open.”
Mr Beggs had been an deputy speaker of the Northern Ireland Assembly and sat on both the Public Accounts Committee and the Infrastructure Committee.
A Queen’s University Belfast engineering graduate, he worked in production management before entering politics.
His first preference vote of 3,549 was well short of his UUP running mate, and poll topper, John Stewart on 6,195.
His defeat erases the Beggs name from local politics for the first time since his father, Roy snr, was elected to the failed 1982 Assembly before going on to serve as MP for East Antrim from 1983-2005.
John Stewart was delighted with his own performance but described his victory as “bittersweet” due to the loss of his party colleague.