This doesn't quite answer your question (I'll address it in a minute) but I think there is another question that needs to be answered besides how to present yourself to prospective employers:

First, on the subject of failing and being the "fall guy." I would try to talk to as many of my former co-workers as possible and ask them for the unvarnished truth about the projects you were on. It is possible, although we hate to admit such things to ourselves, that something about your performance made it difficult for those projects to succeed. It is possible that you are a contributor to their failure, and that the lack of training you requested was not necessarily the issue. I know people who have trouble with projects, and are perennially blaming lack of training or other problems. Next door to them are people who are succeeding, despite having no more training than anyone else. No one writing responses here knows you well enough to know whether this applies to you or not. I have done this before, and as painful as it was, I learned a lot.

On the issue of what you would say to an interviewer, you could say that you were let go because your experience didn't match with the direction of the projects that the company was starting to take, and they didn't feel that internal training was the appropriate solution. This is common, unfortunately.

You could specifically describe a situation where training was not available, but was necessary to complete the job. Don't say it judgementally like this: "I told them I needed training on XYZ and they said no, so they shouldn't have been surprised when my project failed." Say "The project involved the XYZ technology, but unfortunately training wasn't available, and the deadline was too close to allow the project to succeed." If there were more people than you on the projects, say "we were not able to succeed in such a short time" or "we were not able to get the training we needed on XYZ, so we attempted to learn it ourselves and ran out of time". "We" failing is better than "me" failing, and points to a management issue beyond your control.

Use a passive voice - "training wasn't available" - to avoid sounding like you're blaming someone. If they ask why training wasn't available, you can simply say "I'm not sure" and leave it at that. Don't comment on the decisions of management. Let the HR person fill in the blanks in his/her own mind for why training wasn't available.

Focus on the successes and the training you do have, and the experience you think you can contribute to their company. On one hand, they don't want to hire a problem person, on the other hand, some companies just need people and would be happy to have you.

I'm not much of a fan of pro football, but I'm very happy to see Dungy get a super bowl win. He grew up in my hometown, and his family is/was the nicest bunch of people you'd ever want to meet. He's a real class act, and while I can take or leave his religious leanings, it's good to see a nice guy finish first.

Congratulations to Tony Dungy and Good People(tm) everywhere.

Why not just stop calling fouls altogether, unless it is deemed to be egregious, such as an obvious attempt to use your entire body to knock the other guy down. Maybe tripping isn't allowed, or hands to the face. But when someone is shooting a three pointer, and the defender touches the tip of the shooter's finger - that's a foul, baby, the same as if you grab the arm of a driving guard going for a layup, or hugging a player hard to force a free throw in the waning moments of the game.

Figure out what "egregious" means, don't allow tripping or punching, and let them play.

I know the NBA wouldn't like that because scoring would be cut about in half, but we could see what these guys are really made of.

There are plenty of rules in (say) football to protect QBs, punters, receivers, and so on, and they're there partly to help keep those players healthy, but they're also there because they help scoring stay up.

I grew up in Jackson, MI where Tony Dungy was a star athlete (although I was too young to know who he was until he had left town). His mom was a teacher at the high school and was one of my favorites. She was one of the few teachers that treated her students like adults and truly seemed to enjoy what she did in life.

I know this has nothing to do with the topic at hand, but I've always rooted for (and cheered) Tony's success as a coach. Congratulations to him and his team. I think he is probably as good a teacher as his mom.