The Beatles legend tumbled down a set of stairs at the concert in the city's Echo Arena on Tuesday (December 20).
The 69-year-old was not seriously hurt in the incident and "just dusted himself down" afterwards, according to The Sun.
"He's not accident-prone so it's unusual for him to be clumsy," a source said. "He saw the funny side."
The gig was the final date in McCartney's 'On The Run' tour, which he began in New York on July 15 and took to venues in the rest of the US, Canada, the United Arab Emirates and Europe.
He was joined on stage by Rolling Stones member Ronnie Wood at a show in London on December 5.
McCartney announced on Monday (December 19) that he will release a new album on February 6, 2012.
Watch Paul McCartney perform 'Wonderful Christmastime' in Liverpool below: