Look at all the companies that pay minimum wage; they do not like to pay a bit more so those less well off can have it better.
That's far too simplistic. It's not like they can just raise wages with no consequences. There is a trade-off between the amount they pay and the number they can afford to hire. Raising pay at the expense of the number of workers would have the effect of concentrating income, not spreading it around.
Assuming you don't want to cut down on jobs, where do you think the funds for the extra pay would come from? Perhaps you don't think the investors (read: ordinary people with 401ks or IRAs, saving for retirement) deserve a share for supplying the productivity-multiplying capital goods which allows those jobs to exist in the first place?
I think that when you talk about "most capitalists" you have a very select group of people in mind: the fabled "one-percenters". Even within that group I don't think you're giving enough credit—poverty in first-world countries pales in comparison to less developed areas, and that can be attributed largely to the 1% everyone loves to disparage—but in any case the 1% isn't "most capitalists". Anyone with investments is a capitalist. If you have a 401k or IRA, you are in effect playing the part of a capitalist whatever your political views. While that isn't everyone, it is a very large chunk of the population. And most of those capitalists are perfectly happy to donate to charities and help out their neighbors.
In my opinion there are two basic aspects to systematic poverty (not counting temporary conditions). One relates to the individuals themselves, whether it's a matter of priorities, habits, or plain mental illness. Mere habits can be changed, if the motivation exists, but if someone chooses their current lifestyle over getting out of poverty, or lacks the capacity for making the choice in the first place, there is little anyone can do short of an unjustifiable infringement of their right to self-determination. The other aspect comes down to people deliberately tearing down the very capital structures needed to avoid poverty in the name of making everyone equal—equally poor, that is.