How to punish people?

I'm having a blast with this game, but I just can't figure out how to actively punish people. I know that there are moves in fighting games that are plus on block and stuff, but it seems like I can only punish S1 and S2 supers.

It's not like I'm fighting against people that use assists or use specials to make blocked strings safe. Their attacks just hit me way faster, so every game people punish me for trying to punish them if that makes any sense.

So how do I handle this, because I know this is just a skill issue.