Brunt was substituted to ironic cheers as the Baggies went down 2-1 in the Premier League on New Year's Day, and defender Jones thinks the supporters were harsh.
"I don't understand why they did that. You can tell that Brunty, the same as a lot of us, misplaced some passes, but the effort was still there," said Jones.
"He was challenging and working hard. It was one of those days for us individually and as a team, we know that and we'll learn from that.
"But Brunty's a great player, he has been in the past and still is now. He's a massive part of the starting XI and the squad."
West Brom were also booed off at half-time and full-time following a disappointing performance, but they remain seventh in the table and Jones believes they have become victims of their own success.
He added: "The expectations we've put on ourselves, and the performances we've given in front of the home crowd, means they expect that.
"We expect high standards from ourselves, but against Fulham it wasn't a good performance.
"Yes, there were misplaced passes and mistimed tackles, but all the lads gave it a right good go."