The Prime Minister conveyed his displeasure to the home minister on the sidelines of the Governors' Conference at Rashtrapati Bhavan on Tuesday, they said.
The sources said the Prime Minister told Shinde that it was alright to be tough on terror but the delay in informing Guru's family was not how "state craft" is conducted.
The government had sent a letter through speed post, despatched Friday last, to Guru's family in Sopore in Kashmir and it reached them only on Monday, about 51 hours after the execution.
Singh took exception to the decision to inform the family by post, the sources said.
Guru's family has been angry over not being informed in advance about the hanging as they came to know only through the media after the execution was carried out.
Jammu and Kashmir chief minister Omar Abdullah has also strongly criticised the decision to inform the family through post in this age.