One thing to keep in mind about learning things is that different people learn at different rates and in different ways. I can remember on several jobs how it took me a while to understand the job, but once I did, I had it down pat. My learning curve was very flat at first and then shot straight up once the pieces fell into place. You might be like that, and if you are, you need to nicely let your boss know that that's how you function. Don't be afraid to nicely defend yourself. Your boss will respect you more if you do.

With job offers, keep in mind that employers understand that employees need time to learn systems unless you tell them that you already know. And don't claim you can do things that you can't as lying on your resume can be grounds for termination.