"I worry about them all the time," he said in the November issue of Psychologies. "That's the emotional bond and responsibility that sweeps over you when you have a family to look after."
The father of six, who recently tied the knot with Angelina Jolie, went on to say that his children have taught him the true meaning of love.
"I care about them more than I care about myself," said Pitt, 50. "You see past yourself and become more generous and giving, and wanting only the best for your family.”
He added: “You learn to value the basic beauty of family, of watching your children grow and evolve. It's the most beautiful thing you can experience."
The kids even came along for Pitt and Jolie's honeymoon in Malta, where they enjoyed family excursions aboard a luxury yacht, as well as bowling trips and tours of the Mediterranean.
"They had fun with their kids," an onlooker told PEOPLE. "They were friendly with everyone and smiling."