In a message he said that it was a huge shame that the team lost to Italy in a penalty shootout.
“What I have found even more disappointing are the reports about the racist abuse sent to those players whose shots missed or were saved,” said Coun Holt, pictured.
“I find racism reprehensible but also find it ridiculous that these players are heroes one minute and abused the next.”
The Marcus Rashford mural in Withington, Manchester, was defaced with several swear words shortly after Rashford missed a penalty, along with Jadon Sancho and Bukayo Saka, in the 3-2 shootout loss.
An outpouring of support for Rashford, from across the nation, has since followed the vandalism and remarks.
“Thankfully the social media platforms have removed comments and the police are investigating the vandalised Marcus Rashford mural in Greater Manchester,” added Coun Holt.
He added that Pateley Bridge had not escaped its own incidents of vandalism recently.
“Other vandalism, this time much closer to home, has also been a huge disappointment,” he added.
“The recent damage to trees on the Millennium Green was really upsetting and the police are investigating at the Councils request.
“We have managed to save all but one of the trees but the tree that required felling was 40 to 50 years old and it does seem such a waste of a living thing.
“The Council is indebted to Ross Hanley Garden Services for the speed of their response in making the area safe again for everyone to enjoy.”