The whole point wasn't that we're celebrating the fact that we drew the game, it's the fact that Australia didn't win it, which considering the way we batted, I'd call that a good result.
And yes, I think most of the blame for this game was down to our batting. The Australian bowling attack, bar Hilfenhaus and the odd spell of hostility from Johnston/Siddle was pretty average. The ball wasn't swinging, the turn was slow and nearly every single one of our batsman got out. I don't think I'll even bother getting the calculator out but if you look at the runs scored from 6-11 compared to 1-5 it doesn't look good.
Bowling wise, I think Harmison should be given the chance at Lords at the expense of Monty. Swann was excellent over the winter and I'd back him to come back stronger in the next test. I would think about bringing Onions/Sidebottom in for broad as well but that might mean too many changes right now. As for the batting - I can't see any obvious candidates to drop because it's not like we've got a form batsman to come in. Bopara was dissapointing though - he's really starting to look like another Ian Bell, scores stacks of runs when it's easy pickings but looking out of sorts in high pressure situations. If he doesn't score runs in the next test they should look at bringing someone else in, or at least do so before the winter.
It was also a good change to actually be on the other end of one of these results. How many times in the last 5 years have we failed to bowl a side out on the last day, handing them a draw in the process preventing us from drawing/winning a series? SA 2004, Australia 2005, WI 2009...
Edit: I expect Lords will be a draw too, but should get results at Edgbaston and Headingly. I could see this ending up 1-1. We really missed a trick not playing at Old Trafford, out of all the grounds in the country I'd have thought our best chance was there.