With all due respect to a few above, there are suggestions that I don’t see working in a Pungo. Between lack of clear points for control from your thighs and that huge cockpit opening, there are real limits to what you can do with edging or skulling (sculling?) braces compared to being in a sea kayak. Especially if you are a smaller person in a big wide Pungo.
You can do these things to a degree. What is impossible to tell without being there is whether the amount of leverage you can get from these actions in your Pungo would have been sufficient for managing that particular boat wake.
Are you paddling with people in more like touring kayaks? In that case you need to understand they have some maneuvering options that are not so reliable for you, and come up with alternatives. It is a problem that you left the group in responding to the boat wake, because you put yourself away from potential help.
So very first comment, always towards the wave face. Hence you should have planted your paddle on the right side, not the left. And then a fast hard sweep stroke, leaning forward helpful.
Honestly most people get overly concerned about trying to hit a wave dead on. In fact a 45 or so degree angle is easier to achieve in a pinch, and makes for a quite safe, slithery ride. SeaDart is right.
In a proper sea kayak it takes a lot of wave for me to care whether I am full on sideways to it, in fact in some conditions it is the easiest way to travel. But that is not the boat you are in.
If the wake was relatively small, say a foot to a foot and a half, the Pungo would likely have been fine taking them from the side. Or if they were bigger but you caught them when they were rounded at the top rather than peaked with whitecap. As suggested above, it is your job to just stay relaxed and let the boat handle it.
Regardless of how you handle it, boat wakes are something you need to manage. If you can’t get help from a fellow paddler locally take a look at the material under Learn on this site.
Later add, always keep paddling. Kayamedic mentions the same thing I have seen, new paddlers get out into a smidge of wave and freeze with their paddle up in the air. A boat in motion is always better at handling any waves, and the paddle up in the air doesn’t do much to advance that. It needs to be in the water and moving. Keeping the paddle moving helps the paddler stay loose rather than allowing them to fully freeze up.