I am wondering what is the significance of finding a particular protein specific to a disease or control group? when we detect 1000s of proteins in a proteomics experiment, how can one be sure that the specific proteins found in say, a disease group is really absent in control group than by random chance?
You can never be 100% sure that a difference is real and not a statistical fluke. This is the entire concept underlying Type I errors - these are errors where the null hypothesis (usually, that there is no difference) is incorrectly rejected (a difference is called significant, when in fact none truly exists). Especially when performing many hypothesis tests, it's possible that a variable with truly identical distributions between two groups appears to have very different distributions simply due to sampling variability.
You can reduce the chance of making such an error by reducing the level of alpha used to determine significance, and by performing appropriate multiple hypothesis correction. With stringent significance thresholds and conservative correction, you can make it extremely unlikely that a "significant" difference could be due to random chance, but it's not usually possible to conduct an experiment with a Type I error rate of 0%.