Coffee – My espresso shot is extracting too quick, what am I doing wrong

It IS the roast that is the difference. The only real difference in the beans is that some beans taste better at a higher roast than others, so they are more appropriate for espresso. Your Italian grocery coffee company may be using the espresso label for marketing purposes, but in general, espresso coffee beans can be the same beans that are used for "regular" coffee, but roasted to a French or Italian roast level, which is darker than City or Full City.

Since the advent of Starbucks, many roasts are much darker than they used to be. Dunkin' Donuts coffee, which is a Full City roast, used to be the norm, but now a French seems to be what you can buy.

I roast my own coffee and take it to just into the second crack which is, generally, a Full City roast...a point where the character of the coffee predominates rather than the flavor of the roast. There is more information about roasts at Sweet Marias where I buy my green beans, and reading through the site will give you way more of a coffee education than you probably ever wanted.

So, yes, you can use the coffee you have to make brewed coffee. It will probably be roastier than you would normally have, unless it is just a marketing ploy, in which case it will taste normal. Consider how long you have had this coffee; if it has been shelved for a while "normal" probably won't be all that great, since freshly roasted coffee is, generally, way better than old coffee. But as long as the oils aren't rancid, it is more likely just going to be bland.

To answer your question with a straightforward solution, my key recommendation would be to buy a new machine for two reasons: better espresso and milk.

Before all, if you are not willing to invest more than $100 (USD) in a machine (more like $350, but I'm sure you can scrounge for a decent entry-level machine to get the job done), you can stop reading as my suggestion relies on a better machine. That said, quickly browsing Amazon I found a Cuisinart unit with tepid reviews (205 averaging 3.5 stars) on sale for about $80.

Here is what is going wrong with your latte:

• Machine: If you have a Krups it's pressure probably isn't rated. This is a bad sign as it indicates how well it will "pull" (brew, make) the espresso. My guess for most units: Unrated = won't pull. Buy a machine with a rated pressure, 15-bar is what to expect. (I don't mean to sound snobby; I got by with a $60 Coffeemate for awhile, but they won't get you the results you're asking for)
• Bean: Lattes are made with espresso, not coffee (U.S.). You're using coffee. So start by buying espresso beans instead of dark roast coffee or Folgers. While you're at it, if you want it to taste like restaurant quality, buy them from a local roaster (I'd imagine you can get some mad fresh beans in Africa) and grind them fresh (just prior to brewing). I prefer a coarser grind to my espresso, you will also need to press the grinds ("pack") in the gruppa (metal basket of machine).
• Milk: While you're at it, don't necessarily use whatever comes out of the fridge. Here and here have the dirt on milk and frothing. Basically fuller body for the drink use milk with more fat, if not use less fat. If you have a favorite place in mind for your exemplar latte, go ask them where they get their milk and follow suit. There's a degree of preference in which milk you use, go with the one you know you prefer and perfect your technique.
• Frothing/Steaming: You aren't frothing your milk. Buy a machine with a working wand, froth the milk. Actually, frothing the milk is fun and it tastes great all on its own. Note: you do want to get foam on top, this indicates you have properly steamed the milk below (remember to hold back the foam, and pour only the steamed milk into your latte, then depending on your region's definition adding a bit of foam on top).
• Container: Add some dignity to life whenever you can. Use ceramic; you're at home.

Those are the key differences that are causing problems for the latte you want to amp up. Now you can skip the consumer espresso machine advice and get a stove-top setup (espresso pot and use a normal, smallish pot with a whisk for the milk), but that takes a smidge more effort in terms of getting it right. Either way, following these guidelines should get that latte much closer to where you want it to be. Basically, the only advantage the shop will have over yours is a bigger machine, overworked employees who might not have the time to care about your coffee at this time, and paper cups.