The former England striker scored a hat-trick in the win over the Tigers and has now scored five goals for Ian Holloway's side in just his seventh game for the club.
Phillips told the club's official website: "From a team point of view we knew how important this game was, three points is huge for us.
"It puts pressure on the teams around us. I think we've sent a message out to the team's around us."
Palace are just two points behind Watford in second place in the Championship in the race for promotion to the Premier League.