Terry, I think there's the possibility that you're misunderstanding what's going on here. First up, your main expectation is not to be pumping out the same work level as the rest of your coworkers. Like you said, they have MUCH more experience than you do. And they know it - they're not expecting you to do the same thing as the people that have been around a long time; the expectation is that you're learning - how the group works, how to do a good job, the best way to interact with people, what the various areas within the company are, etc. Productivity will come - what they're looking for is that you're going to improve over time until you're the knowledgeable, experienced person in the group. (I like the comment explaining it in terms of a sports team with veterans and rookies.)
Now, for the second facet: your coworkers disappointment. I wouldn't be surprised if you're interpreting this completely the wrong way. They might not be disappointed in your performance - they might be upset that they're having to stop what they're working on to train you in aspects of the job. Some people don't deal with that very well - they "just want to do their job." And it's tough for them - having to break away from whatever they were working on (especially if 'training the new guy' goes against their performance metrics.)
So, here's my advice:
Be on the lookout for things that you already know how to do that will save your coworkers time. Some people don't deal well with, "Ugh, I have to show the new guy how to XYZ now?" But they deal very well with, "Wait, you mean you can take care of ABC for me? Great - I was getting swamped!" One of the reasons I was loved in my area straight out of college was that I did this - small misc programming tasks that didn't require a lot of in-house knowledge could get offloaded from the senior devs, freeing up their plate for more important things.
Make sure the amount of direction/management you require is at a reasonable level. Keep in mind, unless you take initiative, you're not only taking time away from others to train you, but also taking time away from others in figuring out tasks for you to do. Managers hate having to try to come up with lists of things for the new guy to work on. Managers love hearing, "Hey, I noticed that Problem XYZ's been cropping up a lot lately. I've got an idea on how to fix it by doing ABC. Is it okay if I try to develop a fix?" Heck, even, "I noticed that Bob's the only one who knows the ABC process. Would it be okay if I started learning it to help back him up?"
Go out of your way to learn - and ideally in ways that don't require a large time investment from the rest of the group. The main thing separating you from the productive, experienced members in the group is just that: knowledge and experience. Start studying - not only will it make your transition to productive/experienced go faster, but management will love it.
Don't just ask the manager for tasks. Ask the experienced coworkers, too. Ask them if there's anything you can do to help out, anything that they can recommend for you to brush up on learning about, anything that they'd like to be able to offload onto your plate. (Note: you'll still want to run this by your manager to make sure they're okay with it and so they know what you're working on. Coworkers won't set your priorities, but they can help coming up with potential items to add to your plate.)