Police said two masked men entered a house on Margaret Street at around 8.45 pm on Tuesday and shot the man.
The man is receiving treatment for his injuries at Altnagelvin hospital.
Fr Michael Canny said it was a very serious attack but there was no justification for it.
“No matter what issues are at the root of this attack, in any right thinking society, we cannot have people taking the law into their own hands,” he told BBC News NI.
“People cannot act as judge and executioner, there should be only one law and order and that is the PSNI.”
SDLP councillor Martin Reilly described the shooting as “a horrific attack”.
“This type of violence is not wanted anywhere in the city and region,” he said.
“It is very worrying that we have these types of incidents happening across our city.
“Margaret Street is a close knit community, just around the corner from where this attack took place is a children’s play park, it’s a built-up terraced house environment.”He added: “Many people live in this area; anyone could have popped out on to the street to witness this type of attack.”
Any gun attack, he said, can have “tragic consequences”.
Sandra Duffy, chair of the Derry and Strabane Policing and Community Safety Partnership, said people in Derry “are shocked and disgusted at last night’s shooting”.
“The brutal attack has no place in a city which is trying to move forward,” said the Sinn Fein councillor.
“It is clear that the criminal gangs responsible for this type of brutal assault have absolutely no concern for people living here.
“Their only aim is to try to exert some sort of coercive control over the people living in these areas.”
Police have appealed for anyone with information to contact them on the 101 number.
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