You can't legislate for mistakes like Gerrard's, and the second goal didn't matter in the sense that Liverpool didn't score anyway, but Chelsea were only ever going to score in that game if Liverpool lost possession whilst their defence was high up the pitch, which is exactly what happened. Twice.
Of course it was connected to Mourinho. His comments were pretty much "anyone can play with 10 men behind the ball but we try to win the right way." He literally mentioned Mourinho's tactics as a comparison to him playing "the right way."
I'm not saying Liverpool should have played for a draw, but they should have ensure they were defensively sound in their attempts at going for the win.
In the third and final minute of first half stoppage time, at 0-0, when your team only needs to avoid defeat to ensure that you stay clear at the top of the league, there is literally no need for a) most of your players to start streaming forward once you're in possession, b) your two central defenders, who are pretty much on the halfway line, being essentially on opposite wings, and c) for a midfielder to be dropping into the huge gap left between the two central defenders, and upon receiving the ball, frantically trying to turn and move the ball on, despite being under no pressure.
Chelsea had the first chance of the game, five minutes in, and had a further 4 chances prior to the slip. It's hardly like Chelsea had been no where near Liverpool's box before the goal.
Liverpool had looked shaky defensively all season, there's no reason to accept that it was any different in the Chelsea game, and whilst midfielders collect the ball off their centre-backs all the time, they tend not to do it from a squared ball on the halfway line, whilst their centre-backs are pretty much on opposite wings, with the rest of the team streaming forward.
It was incredibly naive to throw so many bodies forward so haphazardly and leave such large gaps between the defenders themselves, and the defence and the goalkeeper, when a draw would have done. You can still try to win without needing your whole team to bomb forward every time you get the ball.