Learn English – How to say when you collect exam papers

Ten minutes have passed.

is the grammatically correct form. Another way to say it is:

Ten minutes have gone by.

There are undoubtedly other ways of noting the passage of a specific number of minutes, but these are the two that come immediately to my mind.

To use the past tenses, you can say:

Ten minutes passed. [simple past]
Ten minutes had passed. [past perfect]

Which form you choose depends on context. Your sentence has no context.

So, the situation is that both person A and person B have brought things to hand out, and both have spent hours on those things, not knowing the other was also doing it; and person B's handouts are clearly superior to person A's?

Then at this point where Person B sees person A realizing that A's efforts are completely overshadowed, B is feeling that it is unfortunate that A wasted all that time doing something that turns out fruitless. Either there is empathy involved (B feels bad because he knows that A feels bad) or there is not (B merely regrets the lost opportunity to have A be doing something useful, or B is happy to outshine A).

If there is some level of empathy involved (and since person B feels "apologetic", it seems that there must be some), then either "felt bad for" or "felt sorry for" would be appropriate and idiomatic.