Kevin Nolan's second half tap-in secured the 1-0 win and the Premiership points for Sam Allardyce's men and inflicted David's first defeat as caretaker manager.
It was no less than Bolton deserved. With Jay-Jay Okocha running the show, the Trotters hit the crossbar on four occasions - Okocha unlucky three times.
Jussi Jaaskelainen denied Robbie Keane in the first half and Jon Blondel in injury but it was Allardyce's day.
David reflected: "Bolton were hungry for success and had a good game plan.
"We didn't start well. Whether or not we were a little drained, I'm not saying we were, but they were sharper than us and we didn't really get into the game in a threatening, attacking sense.
"We were holding them at bay and defended quite well at times but Okocha was excellent and they caused us more problems than we caused them.
"We've got to hold our hands up - we were diappointing, not bright and there was an anxiousness in our play. We never got hold of the ball or looked fluid.
"The lads know they haven't played well, they don't need to be told really.
"We played poorly. We can do much better with the ball and without the ball and although we worked hard, Bolton worked harder. Bolton did better than us and that's how it was."
David Pleat held his hands up after Saturday's defeat to Bolton and admitted: "They were better."