The hosts were two down after 17 minutes to a Bradley Pritchard strike and a Rhys Williams own goal before rallying after the break through Marvin Emnes and Scott McDonald.
Boro, who have tumbled out of the promotion race since the turn of the year, were booed off at the break in their final home game of the season.
"I can understand the fans' frustrations," said Mowbray. "We built up their expectations in the first half of the season and have let them down in the second.
"And I was angry today. Maybe there wasn't a lot riding on the game for us but I told them it was the last home match and I expected a display.
"But we started off very slowly, we started off very badly and yes we recovered to come back after the break and ultimately we got a point but it was still a very disappointing day.
"With respect, in my opinion we should be beating teams like Charlton here at our place. And the fans think so too.
"It has been a frustrating season but we must learn from it. We know next year we need to be tighter and keep more clean sheets and build a stronger mentality within the group."