After netting his first Eagles goal in the 4-1 win, Tomkins was forced off at half time and there were suggestions that he may face a prolonged spell on the sidelines, but Parish has said that the club have received some "good news" regarding the issue.
Parish told The Sun: "We need some more luck than we had with injuries last year.
"We've had some good news with Tomkins this week because it looks like his knee's okay although he went off at half time. We've had a bit of a bad run with injuries, so hopefully our luck's about to turn."
Tomkins had been making his first league start since leaving West Ham United to move to Selhurst Park.