Yet they suffer just as we do. They grow old and die, are divided into prey and predator, etc. Man would suffer and die because of the curse of sin that he had brought upon himself, but man also had an eternal spirit, something animals do not have. Man's spirit would live after death of the flesh, animals' spirits do not. When Man dies, he either goes to Heaven or hell.
Animals simply cease to exist.
Yet God in His mercy made a provision that Man should once again live forever as Adam was originally destined to do. But not in the flesh for the flesh was corrupted because of sin, but in the spirit, which God would redeem when He took His own curse and punishment on Himself through Jesus Christ at the cross. The results of that original rebellion are still with us today. Look around you at the behavior of people, watch the news reports. Millions of people suffer and die all of the time, through war, famine, disease, murders, natural disasters, attacks by animals, etc.