Speaking to BBC Radio 4's Sunday Programme after being stripped of the title reverend last week, Mr Flowers, 66, said his problems were "largely" in the past.
But he said it would be a "lie" to suggest they were completely over.
In 2014 he was fined for having cocaine, crystal meth and ketamine.
Mr Flowers, who became a Methodist minister in Bradford in 1976, has now also lost the authority to lead services for "seriously impairing the mission, witness or integrity of the Church".
He had initially been suspended in November 2013 following allegations in the Mail on Sunday newspaper that he bought and used the illegal drugs.
Along with claims of inappropriate expenses payments, the allegations led to him stepping down from his roles as deputy chairman of the the Co-op Group and chairman of its banking arm.
Mr Flowers told Radio 4: "The truth is that I think all of us struggle with issues of addiction and we have different addictions that affect millions of us in this country,
"I'm not going to tell you a lie that it's behind me totally, because it isn't, but I believe it's now largely behind me, but we still struggle with addiction of different sorts."
Mr Flowers added that his departure from the bank and suspension from the church ultimately made his faith stronger...
Big hugs, Paul.
You can listen to the Sunday Programme programme here.