Newcastle led through William Osula's hooked finish shortly before halftime but Palace substitute Jean-Philippe Mateta scored an 80th-minute equaliser before converting a stoppage-time penalty.
"I always have to look at myself first. I always say that. I'm number one accountable," Howe said.
"There's no way we should have lost that game. We had a younger team today, but that's no excuse. There's enough experienced internationals on the pitch to navigate the defensive aspect well enough."
Newcastle have now dropped 25 points from winning positions this season and Howe was frustrated his players were not finishing teams off.
"Those numbers are incredible. It's blighted our season," he said.
"The fact we haven't been able to consolidate really good passages of the game, but also to go on and score more goals and continue to attack. That's not the tactical instruction we give the players."