Emergency services were called Mr Shaw’s flat on Jedworth Road, Glasgow, at around 5.55pm on Thursday, April 22.
The 45-year-old was pronounced dead at the scene and a murder inquiry was subsequently launched.
Officers previously appealed for any details to piece together Mr Shaw’s last known movements.
He was last seen entering his block of flats around 7.25pm on Wednesday, April 21.
When his friends could not get in contact with him on Thursday, April 22, they went to his flat and found him dead following a brutal attack.
Emergency services were then contacted.
After a ‘disappointing’ initial response, Police Scotland are urging anyone who knows anything about Mr Shaw’s death to "do the right thing” and contact them “as soon as possible.”
Increased patrols are in the area to provide the public reassurance while the police investigation continues.
Detective Chief Inspector Cameron Miller from the Major Investigation Team said: “Unfortunately, the response we’ve received so far has been disappointing.
"I believe that the answer to this murder lies locally and I am again appealing to the local community for any information they can provide.
"Craig was very much a creature of habit and didn’t venture far from his home address.
"This is a busy area and I’m convinced that people will have significant information that will move this inquiry forward, but for whatever reason, they have not yet come forward to speak to us.
“Craig’s family and friends are devastated by his death and the team of officers dedicated to this investigation are determined to trace whoever is involved.
"They are also keen to speak to anyone who visited the block at 6 Jedworth Road on Wednesday, April 21, who has not yet been in contact.
“Any information, no matter how insignificant it may seem, can be passed to officers by phoning 101 quoting reference 2750 of 22 April. Alternatively, phone Crimestoppers on 0800 555 111, where anonymity can be maintained."We have also set up a website that gives members of the public access to a form to send information directly to the Major Investigation Team.”