But Sir Menzies, who took over as leader from Charles Kennedy last year but has failed to oversee an increase in Lib Dem popularity since, said he intended to press on with fighting for "Liberal Democrat values".
"Let me make it absolutely clear; I'll be leading the party through this parliament, through the next general election and into the next parliament," he told the Today programme.
"My strategy for the future is to go on arguing about the need for Liberal Democrat values, about the fact that individual freedom and personal liberty has been under siege from this authoritarian government."
He acknowledged, however, that his party's performance in the English local council elections had been something of a "mixed bag".
After the first results were in, the Lib Dems were up one council in England, but lost one seat in the Scottish parliament vote, despite heavy losses for Labour.
But Sir Menzies sought to focus on what he perceived as positives for the party, highlighting two notable gains in England.
"Obviously I'd prefer it if [the share of the vote] was higher, but I've always said these were going to be tough elections for us and to win Hull from Labour, not just John Prescott's but Alan Johnson's home territory, and to win Eastbourne right in the heartland of the Conservatives, these are two very significant results," he said.
"But I accept it's a mixed bag."
The big winner in England looks set to be the Conservatives, with the Tories having gained 15 councils this morning, while the Scottish National party (SNP) has taken 16 extra seats in Scotland.
In Wales, Plaid Cymru has taken three seats off Labour, which is still the major party.
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