The unhappy manager admitted his team had been second-best in all areas of the pitch.
Summing up Coventry's display, Coleman said: "We were garbage for want of a better word, lacklustre and arrogant. All words you don't want to be associated with and you don't want your team to be associated with.
"As good as we were on Monday at Birmingham, we have gone to the other end of the scale. If we had got anything out of that game it would have been embarrassing.
"We need to have a bunch of players who are strong enough to put back-to-back wins together otherwise we are always going to be in the bottom half.
"We're going to try and bring in some new faces at Christmas time which more."
Coventry fell behind in the eighth minute from a free-kick awarded for Elliott Ward's foul on Craig Beattie.
The impressive Ben Watson swung in the ball from the left and his pin-point ball found Jose Fonte at the far post. The defender's header hit a post and rebounded to the other side of the goal where Clint Hill had a simple tap-in.
Neil Warnock's men might have added to their lead when Shaun Derry took a quick free-kick and when Sean Scannell fired in a shot, Coventry skipper Scott Dann was on hand to block the danger.
The Sky Blues did have the ball in the back of the net in the 40th minute but referee Clive Oliver ruled Clinton Morrison was offside when he prodded in Michael Mifsud's header.
Eight minutes into the second half, Palace scored again. Watson stepped up to fire a free-kick from 18 yards through the home team's defensive wall and beyond Keiren Westwood into the net.
Delighted Palace boss Warnock praised the entire team for their dominant display.
"That's as good as we have played since I have been at the club - even last season when we relied on individual goals because we didn't play football like that," he said.
"We kept possession, we looked a threat and I couldn't fault any department. I thought we were super.
"We're disappointed where we are in the table because it is only down to us. It's nobody else's fault. We should be way higher than this. The lads know how they got to perform and we know we can go anywhere and win if we perform like that.
"I have never seen Ben Watson play or train better like he has in the last two or three weeks. He is a Ray Wilkins type of player. We want him to make things happen and he's looking to get goals which is another string to his bow."