Peas and carrots, ok not to puree?

You don't *have* to puree veg -- you can cook and mash them instead.  If you want them to get the nutritional value you have to break down the cellulose in the veg.  (it's what gives veggies their crunch)

Be careful -- peas and carrots may be common 'veggies' for us but neither of them have a very good calcium phosphorous ratio, so don't let those be the *only* veggies you give and don't give them often.  Variety truly helps you stay safe.

I've been cooking for dogs for years without a food processor.  I cook them and then just use a potato masher.  Don't cook any longer than you need to in order to break them up.

I've done that on occasion when I haven't had time to process them.  The peas seem to be digested fine, but not the carrots.

 I home cook for Jessie using a recipe designed by Mordanna ( Sabine Contreras) and her instructions are to bake or steam all vegetables and then puree them or mash them with a fork. I don't have a food processor either so I mash them. If you see pieces of the vegetables in your dog's stool, you're not mashing them enough. Callie's right about the calcium-phosphorus ratio of some vegetables, but I use a balanced recipe which includes the right amount of calcium to balance the phosphorus.

 The carrots are really going to require a food processor or blender (food processor give you more bang for the buck).  They have little ones that will do the job just fine - right now, believe it or not, I use one that is only a couple of cups to do the food for seven dogs.  I process everything because I add things like jicama and herbs that I really feel don't get broken down sufficiently by the puppers (especially jicama, which is a prebiotic).

I agree about the mineral balance.  The more veggies you add, you'll increase their vitamin exposure somewhat, but you'll decrease their exposure to vital minerals like zinc, copper, and iron (and calcium as previously mentioned).   Adding veggies is actually an excellent way to decrease phosphorus/calcium, which can go way too high with a meat-and-bone based diet.  But realize that it's at a cost to those other minerals, too.