Liverpool and Everton pledged to support police efforts to find those responsible for racist and crude graffiti daubed close to Goodison Park and Anfield.
The Merseyside rivals, who battled out a 0-0 derby draw on Saturday in the Premier League, issued a joint statement in which they condemned the vandalism.
The Liverpool Echo newspaper reported murals and artworks featuring Liverpool stars past and present were sprayed with blue paint, including those celebrating Mohamed Salah, Ian St John and Trent Alexander-Arnold.
The Alexander-Arnold mural was put in place to mark the work done by the Fans Supporting Foodbanks charity.
The clubs said in their statement: "Both Everton and Liverpool football clubs jointly condemn the defacing of buildings and murals ahead of the Merseyside derby.
"Racist and offensive graffiti has been daubed across multiple sites in north Liverpool this morning around Anfield and Goodison.
"Both clubs will work together with Merseyside Police and will support the investigation in finding those responsible. Hate has no place in football.
"Together, Everton and Liverpool football clubs and their supporters will continue in representing our city in the fight against all forms of discrimination."