The visitors fluffed four clear-cut chances to score, while at the other end Darren Ambrose showed them how it should be done when he applied the finishing touch to a sweeping Palace counter-attack midway through the second half.
"When you have chances like that and you don't take them you have a problem, luck has nothing to do with it," said Strachan.
"It's frustrating, just like last week against Plymouth when our best player, Adam Johnson, missed a penalty.
"It's frustrating for me, it's frustrating for the players who work so hard and it's frustrating for the fans."
Marcus Bent, on his full debut, came up with a shocking miss when Johnson found him in front of goal, the on-loan Birmingham striker shanking his shot horribly wide.
Worse was to come when a Boro break left lone Palace defender Danny Butterfield outnumbered four to one.
But Leroy Lita inexplicably opted not to square the ball as his three unmarked team-mates pleaded for a pass and, having been forced wide by Butterfield, shot harmlessly across goal.
"That was a bit surreal," admitted Strachan, "I just thought 'what's going on'?"
Boro were made to pay in the 65th minute when Palace broke the deadlock in style.
From the visitors' corner, Shaun Derry fed Alan Lee, who surged forward and swung in a diagonal cross which Neil Danns nodded on for Ambrose to finish.
Boro should still have rescued a point, but Palace keeper Julian Speroni pulled off a superb save to deny Gary O'Neil as he raced through and also blocked a late shot from substitute Jonathan Franks.
"That was just an average game for Julian," smiled Eagles boss Neil Warnock. "It was a bit hairy at the end and that's when character comes in."
Ambrose took his tally for the season to 10 - not a bad return for a player snapped up on a free transfer after being released by Charlton in the summer.
"I was so pleased it fell to him," added Warnock. "It's not my fault someone gave him away. I bid £1.5million for him once - that's how much I rate him.
"He needs a certain type of manager and we make a good pairing.
"But I think we had 11 stars out there."