Arthur said Moses would go for scans on the suspected eye socket fracture he suffered early in the 54-10 loss to Brisbane at the Gabba on Friday night.
He played on bravely until halftime but medical staff then ruled him out of the match despite the Eels No.7 wanting to play on.
The Eels are in 10th on 26 competition points and to play finals must beat Sydney Roosters (home) and defending back-to-back premiers Penrith (away), before picking up two competition points for the bye in the final round.
Even that may not be enough as the Eels are one point outside the top eight, which could become two points by the end of round 24.
Arthur said his side was not out of the premiership race, despite likely not having Moses for the rest of the round games. Veteran forward Andrew Davey also failed an HIA against the Broncos.
"It makes it tough but we are not giving up," Arthur said.
"We are going to keep fighting until it is over. We have got two games and a bye. We will just worry about next week. There was a bit of carnage there with injuries but we get (prop) Reagan (Campbell-Gillard) and (winger) Maika (Sivo) back next week.
"We will just fight on. This team has been fighting all year and we will continue to fight.
"It is not like we didn't come here to try. Our attitude was on. You could see that in the first 20 minutes. We were just beaten by a team that was too good for us. It's as simple as that."
Captain Clint Gutherson shares Arthur's belief.
"We have a tight knit group here and we are not going to go into the next two games just playing them. We are going out to win." he said.
"Tonight it didn't go our way. We lost Mitch and it looks like AD (Davey) as well but whoever steps in will do the job."
Arthur said playmaker Daejarn Asi, who played centre against the Broncos, would likely play five-eighth and No.6 Dylan Brown move to halfback in Friday night's clash with the Roosters.
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