Worth considering what the manager thought the problems were:
It was a bit Jekyll and Hyde football today, said Klopp. You could see how good we can be. We were incredible in the first 35 minutes. Then after an intense week, away at Arsenal, I dont have any real explanation but the intensity might be one. We became sloppy in the last line.
In the second half we were not compact, the first line pressed too high and the distance was not right, admitted Klopp. We played a high line and did not catch them offside which was our fault of course.
-- separate interview/quotes --
"We looked really sharp and ready to play in small spaces then two or three sloppy passes and the stadium is back, Palace is back and we did not start well in the second half.
"We had our moments but we did not control it any more. If you lose a little bit of focus it showed how tired we could be as Palace played a really good game. We opened the door for them and they ran through."
The word 'sloppy' in the two separate interviews might referring to different things, though not entirely clear; the second is directly about 'sloppy passes' - the first may be the same (Matip's pass is obviously in the last line, Firmino's was also played from deep and between full back and centre back); or could be about the last line positionally, related to the point that the offside trap failed a few times and subjectively, regardless of how high it was, it wasn't much of a line at times.
But the explanation of the second half is in contrast to many of those posting - not that we "didn't press" in the second half, but that the line of engagement was too high, with too great a distance between the lines, not compact. We also pressed very high in the first 35 minutes, but that was counter-pressing, winning the second ball high and quickly attacking Palace. The 'defensive' press in the second half was ragged and made us too open. That presumably explains the substitution of Ox fairly early. We still had a couple of midfielders we could have brought on with clearer instructions to correct that (if Henderson/Jones felt to be particularly at fault), but didn't bring on Milner until after the penalty (though he'd been stood waiting for a few minutes) - and then for Firmino. In Milner's case, possibly he didn't have the legs for much more than that, after a busy period in which he's looked knackered at times; Morton, some hesitation with his inexperience at a difficult stage of the game?
It's fairly easy now for Henderson to get the bulk of the blame, but that doesn't feel quite right: if it were, that would be clearer from selection/substitutions and Klopp's behaviour on the touchline. It's surely about groups of players and the distances/cohesion between them, and I think it's clear that in several aspects the right side - Trent, Matip, Henderson, Ox/Minamino - is less secure, less positionally sound, a little less energetic, than the left. Perhaps more importantly, that would be a common perception that the opposition would seek to exploit. Though from several recent games, they're getting in behind Robertson/Van Dijk too occasionally, but we're perhaps just dealing with the resulting chances better (or are luckier, on small sample sizes) on those occasions.