The striker, who came from Arsenal on loan, thinks the league table is all the incentive his new team-mates will need to get a vital three points.
Although the Baggies face Burnley in an FA Cup replay on Tuesday, Simpson says their main focus is on the clash with the Magpies.
"Newcastle are struggling on and off the pitch so maybe it's the right time to play them. Even though we had a bad result against Manchester United everyone is still confident and hopefully it's the right time for us," he told the Birmingham Mail.
"For a lot of the lads it would be a weight off their shoulders to get out of the bottom three and closer to safety."
Simpson is also buoyed by the spirit Albion showed in their 2-2 draw at Hull when he opened his Premier League scoring account as they came back after a poor first half showing.
"In the first half we didn't really turn up and went 1-0 down.
"When you play teams like Hull you've got to scrap and at the end of the day it was a good result for us."