Animal meat is clearly very high in protein as a percentage of total calories, but so are most of the non-starchy vegetables. Even the grains are close to the percentage of protein required by healthy adults. If you eat a healthy and diverse diet of vegetables, with limited intake of cereal grains, you will certainly get more than enough protein from your diet. In fact, the only foods you can really find which do not give an adequate supply of protein are the processed foods, which tend to be extremely high in carbohydrates and fats while lacking in protein.
For the vast majority of adults, getting adequate protein is simply not something to worry about. Most will get more than the recommended minimum of 12-15%, unless their diet is unusually high in processed foods or grains. Even vegetarian diets easily attain adequate protein and even high protein intake! Just to make this point more clear, here are a couple examples:
If a sedentary 130 lb. woman eats her daily recommended intake of calories (around 1400) in the form of a vegetarian meal, including various vegetables, beans, and grains, then she would consume a minimum of 9% and a maximum of 56% of those calories in the form of protein, depending on how much rice she eats versus mushrooms. Beans and grains are more calorically dense than vegetables, so we’ll assumed that more of the protein will come from these calories. A safe estimate of total protein percentage of the foods put together is 15-20%, to account for both the high-protein vegetables and beans and the low-protein grains.
15-20% of 1400 (her total caloric intake) is 210-280 calories in the form of protein. Protein contains 4 calories per gram, so 210-280 calories works out to 52.5g to 70g of protein. At the low end, this is more than enough protein for a sedentary person of her weight, about 50g (130lbs = 59kg, 59 * 0.85 g/kg = 50.15g protein). At the high end, she has consumed about 20 grams of protein more than necessary!
What if she were athletic? You may have heard athletes need more protein than average, to account for gains in strength and endurance. The recommended amounts listed usually fall between 1.2 g/kg and 1.8 g/kg. It is true that athletes need more protein, but consider the next example, using the same woman but with a different lifestyle.
If the same 130 lb woman was very active, and needed to consume 2200 calories per day to account for the extra activity, her protein requirements would change, but her diet does not need to. If she ate the same overall food, for the same 15-20% of calories from protein, she would consume between 330 and 440 calories in the form of protein, which works out to be between 82.5g and 110g of protein per day. At 130 lbs., this would account for between 1.4 and 1.86 g/kg bodyweight. Thus, as she got more active and consumed more food, her protein intake increased and naturally fell between the recommended guidelines for athletes. It takes no special effort to achieve higher protein requirements if you already eat a healthy diet!