Economists would argue that markets do not actually cause poverty. Instead, they allow poverty to occur. Economists would then argue that markets allow greater overall wealth to exist in an economy than would exist in a command economy.
Economists argue that poverty is caused by various sorts of inequality. Most typically, these are inequalities in skills. A person may become poor because his or her skills are insufficient to allow him/her to compete in the market. Alternatively, the person's skills could be a bad match for the kinds of jobs that are available.
In either case, the market is not creating the poverty. The poverty is caused by the person's lack of skills. To use a sports analogy, saying the market causes poverty is like saying that playing a game causes one team to lose. Playing the game gives a team the chance to lose, but it is other factors that actually cause the team to lose.