The support for 52-year-old Davis in his 30th year of competing at the Crucible has grown since he knocked out defending champion John Higgins on Saturday.
Robertson admires the achievement as much as anyone but is unlikely to be handing out favours in their last-eight clash which begins tomorrow morning.
Barry Hearn, who manages Davis and chairs the World Professional Billiards and Snooker Association, has led calls for the six-time former world champion to be knighted.
Robertson backs that, and said: "What more can Steve do? Not only on the table but also with the stuff he does off the table, it's fantastic seeing such a great ambassador for the game putting so much back into it."
The Australian explained: "He's won so many tournaments and for him to be able to pick himself up and practise so hard for this event, and to beat the world number one the way he has, is absolutely amazing and an inspiration for anyone who thinks they're coming to the end of their career."
Robertson scraped through to the quarter-finals after fighting back from 11-5 down to beat Martin Gould 13-12.
And he insists he will be prepared for any such similar situation in future at the Crucible. "These sort of results hold you in good stead for the rest of the tournament."
Former champions Ronnie O'Sullivan and Mark Williams were facing a nine-frame shoot-out in their second-round tussle this afternoon after finishing deadlocked at 8-8 last night.
Williams let an 8-6 lead slip away as O'Sullivan punished his mistakes. O'Sullivan had looked only half-interested at times but did enough to remain on level terms, after they had shared the first eight frames of the match on Saturday.
Stephen Hendry missed a big chance to develop a lead against Mark Selby and had to settle for 4-4 after their first session.
Hendry, 41, looked certain to go 5-2 ahead with one to play when he led 75-0 in the seventh frame, but Selby managed two snookers and potted all the balls to win it 77-75.
Another former world champion, 2005 winner Shaun Murphy, trailed 5-3 against Ding Junhui who made breaks of 68, 103 and 78.
Morning and evening sessions will decide both the Hendry-Selby and Murphy-Ding matches today, while Ali Carter, the 2008 runner-up, will attempt to convert a 10-6 lead over Joe Perry into victory this afternoon.