Andy Boddington, Lib Dem councillor for Ludlow North on Shropshire Council said Mr Farron had let his personal views intrude and fought a "lacklustre" campaign in the run up to the general election.
Mr Farron quit on Wednesday, saying he could no longer reconcile his strong Christian faith with his leadership of a liberal party and various former ministers are now being touted to take part in a forthcoming leadership contest.
Councillor Boddington said Farron had been popular with party members previously and still had a future in politics, but it was time for him to go as party leader.
He said: "Tim Farron’s position has been untenable since the election result.
"He made significant errors during the election campaign, including allowing his personal views on gay issues to intrude into a national campaign. We are a liberal party with liberal views on sexuality. Tim acknowledged that but weakened under the media campaign against him during the election.
"Tim headed up a lacklustre general election campaign. I haven’t heard much support for him on the Liberal Democrats internal social networks.
"He was popular inside the party. He oversaw a huge increase in membership after the disaster of the 2015 election.
"I think he has a huge role in the Liberal Democrats in the future. He is a great cheerleader and can galvanise people into getting winning local campaigns underway. I am sorry he didn’t flourish as a party leader but he has done the right thing by resigning tonight.
"There will be inevitable speculation about who will be the new leader of the Liberal Democrats. At this early stage I favour Jo Swinson, the re-elected MP for East Dunbartonshire. She has the leadership skills and charisma that are needed to lead a Liberal Democrat revival," he said.
Swinson, a former junior minister in the coalition government is the bookie's favourite to win a leadership contest.
Former ministers Sir Ed Davey and Norman Lamb are also expected to contest the Liberal Democrat leadership, with ex-business secretary Sir Vince Cable speculated to take over on a temporary basis in the interim.
During the campaign, Mr Farron was asked repeatedly in media interviews to clarify his views on gay sex given his strong faith.
Announcing his resignation he said he was "Liberal to his tips" and was passionate about allowing people to live the lifestyle of their choosing. But he said he found it difficult to keep having to justify his Christian values while still being leader.