I don't think that they necessarily "wanted it more", I would be surprised (and indeed devastated) if that was the case. I just think that Bilic got his tactics spot on and won the battle between the two managers. We could've exposed this without even changing our system, but were not brave/skilled/experienced enough to play through their press. Bilic's system kept our fullbacks largely pinned back with anything we did go forward with then being funnelled into their central defensive three. They pressed Lloris so that his kicking was poor and they pressed our two centre halves and Dier to make it difficult for us to build from the back. Of course the boggy pitch didn't help in terms of us being able to play it through the press, but even had it been a good pitch, without Dembele and Alli we lacked the players with the confidence, strength and skill to demand the ball in central areas and be able to keep it. Had we got through that initial press we would've seen our attacking midfield three and Kane up against only the three West Ham central defenders, but we didn't exploit this at all in the first half. I thought that Mason got involved in a battle instead of trying to ensure that we played our football. All it needed was for one of our central midfielders to be able to draw a foul and booking from Noble and/or Obiang and the whole dynamic would've changed.
Knowing that West Ham couldn't keep up that level of pressing for the entire game in the second half, Bilic then instead sat them back into a very well organised defensive position. I thought the problem for us was that as the game wore on we didn't have the right creative players to take advantage of their defensive tactics - I would've liked to have seen Lamela still on the pitch and Chadli entering the fray in the last third of the game when pressure builds, space opens up and we have more and more possession in and around their penalty area.