Preheat oven to 350 degrees F (175 degrees C). Grease a 9x5-inch loaf pan.
Place carrots, celery, onion, garlic, Italian seasoning, and black pepper in a food processor; pulse until vegetables are minced. Transfer vegetable mixture to a large bowl.
Process chicken tenderloins in the food processor until ground.
Stir eggs into vegetable mixture using a fork until incorporated; add half the tomato sauce and mix. Fold chicken into vegetable-tomato sauce mixture; pour into prepared loaf pan.
Bake in the preheated oven for 1 hour 30 minutes; spread remaining tomato sauce over meatloaf. Continue baking until meatloaf is cooked through, about 30 more minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Let cool in pan for 20 minutes before slicing.
