International Development Secretary Priti Patel called on Conservatives to work to win the trust of "the ordinary working people across the United Kingdom" in May's local government elections.
Trudy Harrison won the Cumbrian seat from Labour in a by-election last month, with Ms Patel hailing the result as "almost unprecedented".
She said: "Jeremy Corbyn's UK Labour Party have managed to lose a seat that even Michael Foot held on to.
"As a movement, be it UK Labour or Scottish Labour, they are simply no longer credible. They are too divided and, quite frankly, too incompetent."
She went on to say the victory in Copeland showed that "this is a Government squarely on the side of working people".
Ms Patel continued: "We have a driving mission, a conviction, to build a country that works for everyone and not just the privileged few.
"This is the Prime Minister simply getting on with the job and offering calm, firm and stable and competent leadership at a time when that is exactly what the British people are crying out for."