In the 12th minute at CommBank Stadium, Kiraz injured the medial cruciate ligament in his right knee when his legs became twisted in a three-man tackle.
Kiraz led the Dally M Medal leaderboard after three rounds and would be a significant loss to a Bulldogs side already missing first-choice winger Josh Addo-Carr.
Viliame Kikau, Luke Thompson, Nu Brown, Chris Patolo and Franklin Pele are among the others sidelined.
"Obviously (Kiraz) not being able to finish the game is not a good sign," Ciraldo said.
"Hopefully we get some good news there. We're not getting much luck at the moment in any sort of area."
Kiraz's substitution forced the Bulldogs to reshuffle their backline, which allowed the Eels to capitalise.
Parramatta began exploiting the makeshift edges, scoring three tries down the flanks in six minutes to open up a 16-0 lead at halftime.
"It definitely affects the whole cohesion of the team," Ciraldo said.
"This club is built on determination and grit and we're showing plenty of it at the moment.
"In the future, whether it's in six months or one year or two years, we're going to look back on this period and it's going to be the making of some of these guys."
Parramatta were never again as clinical as in their six-minute skirmish but the buffer proved decisive.
"I felt like we probably should have went on with it a bit more in the second half," said Eels coach Brad Arthur.
Only minutes after Kiraz went down, centre Jake Averillo injured his kneecap in a tackle from Eels winger Maika Sivo but hobbled on.
"Jake was battling," Ciraldo said.
"There are a couple of other guys out there battling that probably shouldn't be playing at the moment but they're playing because we need them to play."
The Eels' forward pack leader Junior Paulo made a solid return from suspension but it was his front-row partner Reagan Campbell-Gillard who was the most troublesome for Canterbury.
The depleted Bulldogs began dreaming of a comeback in the second half when Matt Burton sent a grubberkick along the ground for Paul Alamoti, who scored his first NRL try.
But Campbell-Gillard shut the door on the Bulldogs when he barged through three defenders for a try under the posts.
He finished with a game-high 198 metres, the performance coming after he spent time in hospital this week for personal reasons.
"He was probably a little bit disappointed with how he played last week," Eels captain Clint Gutherson said.
"We always knew he was going to come out and give that type of performance."
Maika Sivo iced the win with his second try in the final minutes, ensuring he will finish round seven with nine tries for the season and atop the NRL's try-scoring charts.
Canterbury recruit Reed Mahoney had an disappointing first game against his old club, dropping the ball from dummy-half in the lead-up to what could have been a Matt Burton try and conceding a penalty for a late hit on Mitch Moses.
"It's extremely hard when we shoot ourselves in the foot," Mahoney said.
"I know how good this football team can be. We've seen it, we've trained it all pre-season and we've showed it multiple times during the year."
