Wearing the five-eighth jersey, Talagi marshalled Moses' right edge on Easter Monday after the Eels' creative architect was diagnosed with a foot fracture last week.
The teenager had some strong moments in only his second first-grade game.
Talagi notably put Clint Gutherson through a hole to give Parramatta a shot at Wests Tigers' line in their first set of the day.
He looked dangerous with the ball thereafter, though Dylan Brown and later Gutherson took on the bulk of Moses' usual kicking workload.
High-school classmate and rival half Lachie Galvin beat Talagi on a line break that led to Jahream Bula's try, hoisting the Tigers back into the contest.
After that an Aidan Sezer field goal iced the TIgers' 17-16 win in the dying minutes.
In all, Arthur was pleased with Talagi's first hit-out as the Eels face the possibility of missing Moses for as many as seven more weeks.
"He's a young kid, he's learning," Arthur said.
"We've always said that. He's played two games. He'll be fine."
Known for his running game, Brown also threatened to breach the Tigers' defence throughout the clash at CommBank Stadium.
Arthur would not put the loss on his new-look halves combination.
"We can't be blaming them," he said.
"It's a team effort right across the whole field. We had enough ball, we had enough opportunities, we just didn't ice our plays."
Arthur said the Eels' attitude towards the game, not Moses' absence, had cost them.
Parramatta conceded two tries in five minutes midway through the second half as the Tigers stormed back into the contest.
For their part, the Eels had 29 play-the-balls in the red zone during the first half alone, but could not make the weight of possession count.
"I think if your mindset is a little bit different, then execution probably sticks," Arthur said.
"The last couple of weeks, even our loss to Penrith, we've played tough and we've rolled our sleeves up. But I think we were chasing a soft win."
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