I agree with everything you say, but when things aren't going well, the crowd will normally react positively to a bit of intensity in the play, especially when we don't have the ball.
In the first half, there was precious little of that, which was partly due to enforced changes due to injuries and partly due to tactics or the players not following instructions, so I can see why there was booing at half time.
Second half, we were a lot better in terms of effort put in, and the booing was probably more for the result than anything.
Generally supporters will put up with a poor performance when they see the effort being put in. That doesn't mean we need to do a Dogs of War impersonation, but you do sometimes have to be seen to graft a bit on the pitch, even more so when you're not playing very well.