Where would vegetarians/vegans get a substitute of hemo/myoglobin from?
The following informations is taken this source. It also lists some references. If this doesn't answer your question let me know in the comments.

Iron is found in food in two forms, heme and non-heme iron. Heme iron, which makes up 40 percent of the iron in meat, poultry, and fish, is well absorbed. Non-heme iron, 60 percent of the iron in animal tissue and all the iron in plants (fruits, vegetables, grains, nuts) is less well absorbed. Because vegan diets only contain non-heme iron, vegans should be especially aware of foods that are high in iron and techniques that can promote iron absorption. Recommendations for iron for vegetarians (including vegans) may be as much as 1.8 times higher than for non-vegetarians.

Some might expect that since the vegan diet contains a form of iron that is not that well absorbed, vegans might be prone to developing iron deficiency anemia. However, surveys of vegans have found that iron deficiency anemia is no more common among vegetarians than among the general population although vegans tend to have lower iron stores.

The reason for the satisfactory iron status of many vegans may be that commonly eaten foods are high in iron.For example, you would have to eat more than 1700 calories of sirloin steak to get the same amount of iron as found in 100 calories of spinach.

Another reason for the satisfactory iron status of vegans is that vegan diets are high in vitamin C. Vitamin C acts to markedly increase absorption of non-heme iron. Adding a vitamin C source to a meal increases non-heme iron absorption up to six-fold which makes the absorption of non-heme iron as good or better than that of heme iron.

Fortunately, many vegetables, such as broccoli and bok choy, which are high in iron, are also high in vitamin C so that the iron in these foods is very well absorbed. Commonly eaten combinations, such as beans and tomato sauce or stir-fried tofu and broccoli, also result in generous levels of iron absorption.