I've been put in enough high pressure situations to know that the phrase "there's nothing I can do" is rarely acceptable. A good teammate is someone who can successfully problem solve 99.9% of the issues that arise. Some issues are harder to diagnose, some take ordering a piece of equipment, but rarely is a problem unsolvable.
Often times this statement is invoked when the amount of work to troubleshoot exceeds the pay someone is received to solve it. But good customer service does not strive to match pay, it strives to make things happen. At Starbucks if you don't like your drink, they will 99% of the time replace it free of charge. Technically, they don't have to do that. They don't need to remake your drink or give you a refund. But they do, and that's why they're immensely popular.
Don't be so quick to admit defeat when diagnosing a problem. Ask for more time, suggest alternatives, make the effort for any "last resort" options, but only throw up the white flag when absolutely every possible avenue has been explored.