In his first game in charge, Edinburgh raced into a 13-3 half-time lead with summer signing, Argentine prop Augusto Allori scoring a try before Ospreys mounted a creditable comeback.
Afterwards, Robinson, credited as being the most successful northern hemisphere coach of the modern era, praised his new side, but highlighted the need to translate their enthusiasm into efficient game management.
Robinson said: "We"ve got to accept that this is a young team and mistakes are going to happen. We"ve got to accept there will be days when we have very good results and other days when we have disappointing results.
"What has really impressed me afterwards is that everybody is pretty disappointed. Yet we still came away with two points and a draw against the Magners League champions. That shows the attitude we have got here at Edinburgh.
"I don't want big statements made, but the enthusiasm this team trains with and plays with has been 100 % and that is a great quality to have. Credit must go to Henry Edwards and Rob Moffatt in the way they have brought the team together through difficult times.
'the leadership of people like Simon Cross, Matt Mustchin and Ben Meyer has stood out, they have all worked really hard to create a team bond in difficult circumstances with the World Cup players away. There is plenty to work on, but that is good and that positive.
"Mistakes are going to occur here when put under real pressure it is now down to how the boys respond. Do they respond by saying; 'that is as far as I think I can get to?" Or do they respond by getting out on the training pitch and really working hard to prove in a month's time they have improved and can play under pressure. It is a learning experience for us all."
The media's man-of-the-match was Edinburgh's stand-in captain Ben Meyer and Robinson outlined why the Kiwi half-back was handed the armband and applauded the 29-year-old's contribution.
He added: "I thought Ben, while playing as captain, had an assured game. He is a strong character and difficult to knock over. With Ospreys swarming as they did, I was really pleased with how he managed to get the ball away.
"A scrum-half is an important leadership position and he is there to do the talking plus he really understands the game well. I think it is important to give him that opportunity."
Famed for assembling England's awesome pack that won the World Cup four years ago, Robinson admits he has been impressed by Edinburgh's forward division so far and underlined the side's greatest strength " sheer hard work.
He said: "My first impression of Edinburgh's pack is they are very hard working. The line-out functioned well against Ospreys which was very pleasing and the scrum was also a positive.
'the players should be pleased by our set-piece play and the amount of ball we turned over from the Ospreys. It is then about the defensive and attacking qualities and there is the potential there to develop that."
Edinburgh: Tries: Allori. Cons: Godman. Pens: Godman (2).
Edinburgh: De Luca, A. Turnbull, Cairns, Houston, Maxwell, Godman, Meyer, Allori, Kelly, G. Cross, Hamilton, Gissing, Mustchin, Rennie, Reid.
Replacements: Laidlaw for Meyer (61), Lawrie for Kelly (73), Grant for G. Cross (58), Newlands for Reid (53). Not Used: Pringle, Warnock, Dey.
Ospreys: Tries: Vaughton. Cons: Owen. Pens: Connor, Owen.
Ospreys: Terblanche, Vaughton, Taylor, Henson, Brew, Connor, Roberts, James, Hibbard, Griffiths, Bateman, Evans, Smith, Tandy, Tiatia.
Replacements: Owen for Connor (53), Phillips for Roberts (53), Bennett for Hibbard (49), Millward for Griffiths (53), Gough for Bateman (59), Lewis for Tandy (57). Not Used: A. Bishop.
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