Mr Anderson said he was angry his track record "wasn't good enough".
Unite Union aide Dan Carden, 30, has been selected in the safe seat.
Ben Williams, the secretary of the constituency party, tweeted he will resign in protest at a "disgraceful undemocratic stitch-up".
Steve Rotheram, the constituency's MP since 2010, said he was standing down from Westminster after being elected mayor of the Liverpool City Region last week.
Mr Carden, who joined the Labour Party while at school, was selected by Labour's National Executive Committee.
He is an aide to Len McCluskey, general secretary of the UK's largest union, Unite.
He was born in Liverpool, but critics argue he is inexperienced in the city's politics compared to the other candidates.
Mr Anderson, who was on the final short list along with Mr Carden said: "I put myself forward for the selection in Liverpool Walton on my track record of running a successful Labour council in a major city and my desire to use those skills for Walton, for Liverpool and a new Labour government.
"Apparently it wasn't good enough for the panel."
Mr Anderson said he had turned Labour's fortunes around in the city, leading a socialist council and protecting those most in need.
North West Euro MP Theresa Griffin had also put herself forward.
Labour won Liverpool Walton in 2015 with a majority of more than 27,000.
Liverpool Mayor Joe Anderson has said Labour "is not always a meritocracy" after being overlooked as the party's Liverpool Walton candidate for the general election on 8 June.