The former Stoke City gaffer replaced Ian Holloway at Selhurst Park in November and has since seen the Eagles move out of the relegation zone, culminating in a 1-0 win over pre-round league leaders Chelsea on Saturday.
When asked if Pulis could be the manager of the season, Parish told Sky Sports: "Why not? I don't know where we were when he came. We were probably bottom, but Tony would be the first to say that once we've achieved something then that would be a fantastic accolade.
"But he's very focused on trying to keep us up. After Saturday, the real key is to not get complacent. We know where we're at, we're not deluding ourselves because we've had one great result. We've got to keep on performing like that and we need a bit of luck."
Palace currently sit 16th on the Premier League table on 31 points from 31 fixtures, five clear of the drop zone.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball