The Baggies took a huge stride towards survival in the Barclays Premier League with victory over West Ham in their last outing.
They have only been beaten in one of their last five games and can now secure top-flight status with one more win, although results elsewhere may mean even that is not necessary.
Pepe Mel's men travel to Arsenal on Sunday before facing Sunderland and Stoke.
Dawson told the club's website: "There are obviously three games to go now and nine points up for grabs. We want to finish as high as we can and get as many points as we can.
"We've got a great squad and a bit of confidence. We're in a good run at the moment and the fans are right behind us.
"We've just got to keep it going for the last three games and finish it off well."