The former PSV Eindhoven defender signed for Stoke last week.
Cartwright said: "As much as you want to do the right thing and sign English players, you have to look at the best options for the club.
"We would have loved to sign an England international, but we couldn't have signed anyone of that ilk for that price.
"We are not only looking at players from abroad. We did look at other options including certain English left-backs.
"But we feel this is a good deal. It's unusual to get a Dutch international for that price."