I think that it's difficult to say that Dumbledore is to blame for Tom's upbringing. Yes, he could have done more to guide him on a better path, but potentially so could countless others.
Whilst Dumbledore may have been one of the only teachers/adults to see Tom's dark side, Slughorn definitely got at least a hint of it when Tom was being incredibly manipulative in getting information about Horcruxes from him. I don't see him as any more or less to blame.
I think what is more telling is that Dumbledore himself feels like he is partially at fault. Whenever he discusses Voldemort's childhood, he always refers to him as 'Tom' or 'Riddle'. Clearly he's remembering him as a relatively normal child, rather than the monster he became.
Particularly after the ordeals with his sister & brother and Grindelwald, he was possibly particularly sensitive to thinking back and considering how he could have done things differently. He had a lot of regret for a lot of things, and it feels like it's quite clear that Tom Riddle was one of them.
It's also possible that he feels like he could have done more to stop Harry's parents being killed. Whilst it was far from being his fault, again due to his sensitivity it's likely he would have took a portion of the blame onto himself.
The fact that Dumbledore puts so much effort into rectifying these things that he did wrong shows that he feels remorse for them. He did a lot to try and stop Voldemort when he returned, putting his own reputation on the line in order to support Harry's accusations that he was back, and eventually losing his life for it as well.
Overall I think that he spent so much effort on Harry to try to prove that he didn't do anything wrong with Tom. Harry grew up in an incredibly abusive environment, and he could have easily headed down a darker path. He was very nearly put into Slytherin, imagine if he'd been friends with Malfoy, the two would have been an unstoppable pair of potentially dark wizards.
Dumbledore tried to not have any direct effect or influence on Harry at first. He used Hagrid and McGonagall to try and steer Harry in the right direction early on without personally intervening, to try to prove if he did not directly interfere in Harry's early upbringing, he could turn out good, just as easily as Tom turned out bad. That would admonish him of any guilt he felt, as it would have been the person, not the upbringing, that ultimately decided their fate.
TL;DR: Whilst it's almost impossible to say whether Tom was inevitably going to turn out evil, Dumbledore did everything he could to try to prove that Harry, in similar circumstances, could turn out good. This is so that any responsibility he felt for the rise of Voldemort could be diminished by Harry turning out good and ultimately leading to his downfall.