A second half header from Peter Crouch proved the difference between the two sides as Hull slipped to their first defeat in four matches.
The result leaves them just a point ahead of 16th-placed Sunderland but Dawson hopes Hull can build on their good recent form at home.
???Our last three results in the Premier League ??? City away and Villa and QPR which were two massive games that we won ??? gave us a lot of belief coming into this game that we could come here and get a result.
???Now we???ve got to look to Sunderland on Tuesday. Sunderland is massive. Both teams are fighting for survival and they come to the KC and we???ve got to pick ourselves up quick and go again.
???Yeah I suppose it does (make that game even bigger given the defeat at Stoke). But Sunderland will be saying the same after their result today.
???All we can do is concentrate on ourselves and hopefully continue our run of good form at home that we have been on in recent games, but Tuesday is a big one.