The Bees have been excellent proponents of dead ball situations in attack this term, but the shoe was on the other foot when they travelled south of the river.
Palace opened the scoring through a free-kick, as Jean-Philippe Mateta headed home, before Nathan Collins diverted a long throw into his own net after the break to seal all three points for the Eagles.
Defeat brought the Bees back down to earth following their thrilling 3-2 win over Liverpool the previous week and Andrews cut a frustrated figure at full-time following a fifth loss in the league this season.
"\[We're\] clearly disappointed. It was a game of very few chances," said Andrews.
"The first goal was a set-piece where they get first contact and second contact, so we’re clearly not going to be happy with that as we set the bar very high from set-pieces. We probably should have dealt with that better than we did.”
Collins’ unfortunate own goal six minutes into the second half proved decisive, as Palace took a two-goal lead and control of an otherwise largely uninspiring contest at Selhurst Park.
Andrews placed no blame on his fellow Irishman but was left disappointed at his side’s play in attack, as they mustered just six shots all afternoon.
“We huffed and puffed a little bit and didn't have that conviction to our play,” he reflected.
"We didn’t hit the heights that we have in recent weeks individually and collectively, but you have to factor in the opposition and how they tried to stifle the game.
“They are very good without the ball, at denying space and I thought we didn't quite come up with the ideas to really hurt them.
“There was very little in the game, they edged it with the types of goal.”
A positive for the Bees was a Premier League debut for Reiss Nelson, following his loan move from Arsenal in the summer.
The winger made a strong impression in just 15 minutes on the pitch in place of Dango Ouattara and Andrews hopes there is more to come from the 25-year-old.
"Reiss showed real moments of quality,” he said. “We saw glimpses of it during the week against Grimsby where I was really happy with his performance, the intent, the way he tried to play the game.
“He was really dynamic and positive and I thought you could see that again tonight with the class that he has.”