By now, you've probably already realized that you should've done a little research before you plunked a new dog down into your household -- you should've been more careful about how you introduced a new dog to your resident dog -- so I won't batter you anymore with that. :-)
Short answer to your qusetion: If you do things right, and take extra time & care, your older dog will adapt to your puppy, and all will be ok. The fact that your older dog is not aggressing, but is just letting you know he's very unhappy, is a great sign that your older dog is an awesome creature, who's willing to go along, if you will only do your part by keeping the puppy from badgering him.
Picture yourself, 22 years old, in your first apartment, all to yourself, and suddenly, someone dumps a 2-year-old toddler at your place and says, "Deal with it." That 2-year-old is constantly getting into things, and pestering you, and whining -- he doesn't know the rules of the house, and is so flipping annoying!!! Not to mention, he frequently becomes smelly and needs a diaper change -- so you have these stinky, nasty diapers at your perfect, first apartment that you'd set up "just so." Yet, you have to take care of him now! Can you imagine how frustrating that would be?
That's how your older dog feels right now, because you just plunked that puppy down in his face and basically said, "Deal with it, older dog." The puppy is constantly wanting to play, so is probably pestering him and nipping at him and just being an annoying, pesky pain in the a**. The pup is probably having lots of accidents around the house and is just, in general, being an annoying toddler to this older dog who thought he'd had a perfect life with you.
You need to 1)Protect your older dog from the puppy's energetic advances; 2)Take extra time to wear out the puppy's energy -- Obedience classes highly recommended; 3)Make sure you never, ever redirect attention from your older dog to the pup...for example, if you're petting your older dog and the pup ambles up, ignore the pup and keep petting your older dog. If the pup starts bothering the older dog, make the pup stop that, and continue to ignore the pup.
Then,as you're following the above advice, start giving your older dog small treats (like some pieces of cat kibble - dogs love cat kibble because it's usually higher in protein and intensely flavored, and YOU can love it because it's available in very small bags, much cheaper than commercial dog treats...and it's small enough so you can treat often without getting your dog fat). Give your old dog those tiny little treats whenever the puppy is nearby, whenever your old dog isn't reacting negatively to the pup. You want to reward ONLY positive or neutral reactions -- you never give the dog treats if he's curling a lip or staring at the pup, or growling. Only if he's acting cool and calm and happy, while the pup is nearby. The idea here is to associate positive, happy things: "Puppy near me = I get treats! Cool!" (Eventually, the dog will associate puppy = cool, without you needing to treat.)
Please read "The Other End Of the Leash" by Patricia McConnell; it will really help, and will explain this better than I can.
Bravo to you for caring enough to write a forum for help. You care about both your dogs, and that's a HUGE first step. Both of your dogs are lucky to have such a caring person as you for their owner. And, in time, they will both be happy, if you do the right things to help them out. Just always remember to give your old dog a heap of credit for being such a good sport for dealing with the messy, rambunctious, smelly toddler. :-)
Best wishes, and good luck!