Liverpool fan here just some thoughts about the match and the offside situations that has been discussed over the last few pages.
Coutinho was behind the ball when he "received" it from Sterling, so he clearly was onside. Same goes to Sterling's goal against Cardiff, he was aligned (is that how you say it?) at worst. Watch MOTD from last week, they stopped the action both occasions (Henderson passes to Suarez, Suarez passes to Sterling), it wasn't offside.
About our performance. Some of you said we played "out of our skin" and you weren't at your best, yet you beat us. Firstly I don't think you can separate these two and say you'd have humiliated us should you played the way you did before. You couldn't play yout best football mainly beacuse of the way we pressed, not just because your players had an off day. You could say Arsenal played attacking football too, which is true, but their pressing was awful that day compared to ours. Secondly, we did not play "out of our skin". We did well as a team, but none of our players had a good game personally, let alone play out of their skin. Coutinho, for example, is still searching himself and missed an absolute sitter, Sterling also. Kompany kept Suarez quiet too. It's a compliment to the Belgian as well of course but still, Suarez could've played better (even if he created a few for his teammates, he was far from his best). Our midfield also did well together, but none of them played at their best, all made bad choices in front of the goal, and Lucas, for example, had 1 tackle all in all. Hardly a great performance. Defensively we were as shaky as always, maybe more, and Mignolet did awful at both of your goals. My point is that while we did ok overall, worked hard and our tactics was spot on, it was far from our best performance this season, we could've played better.
It was a good game, don't get me wrong, but I think neither team played as well as they could have. I feel a draw would've been a more fair result, but you did just enough to see us off, and we weren't clinical enough to take a point, so a deserved win overall. You play some fantastic football, have a great squad and a clever manager so when you win the league in May (and I'm pretty sure you will), it will be fully deserved.
Good luck fro the rest of the season.