Nevertheless Mr McKenna has welcomed news that such a post looks set to be established by 2019.
A shadow combined authority was formed this summer comprising 14 of 15 county, unitary and district councils, with only Wyre council declining to get involved in any devolution deal.
County Council leader Coun Jennifer Mein predicted an elected mayor could be in post by 2019, if the devolution deal gets the go-ahead from Government.
Liverpool and Manchester are set to elect mayors next year and Mr McKenna, Chief Executive of networking group Downtown in Business, who has been campaigning for an elected mayor for a decade, said: “It would be a nonsense for Lancashire to allow Liverpool and Manchester to have powerful figureheads in the name of elected mayors and expect its voice to be as loud in the corridors of power in Westminster....Business will generally welcome this news; but I would still urge the shadow combined authority to look at accelerating the process, maybe getting a mayor in place by 2018. Being two years late to the party is hardly a great performance, is it?”
Coun Peter Rankin, leader of Preston Council, said: “My personal view is that if the devolution proposals we have put to government are accepted then if we have to accept an elected mayor in order to achieve that devolution then we accept it.”