The Pro12 leaders will be without a host of first-team regulars, including most of their pack, for Saturday's European Champions Cup game against Glasgow Warriors.
Pivac was already without long-term absentees Liam Williams and Scott Williams.
"At my age you don't lose too much sleep over it," Pivac said.
"It's about saying 'here's an opportunity' for some more players."
Prop Rob Evans, hooker Ken Owens, flanker Aaron Shingler, lock Jake Ball will miss the trip to Scotland.
Forward John Barclay will also miss out on facing his former club with a shoulder injury while wing DTH van der Merwe will be absent.
Flanker James Davies has been ruled out for up to 12 weeks with a foot injury he suffered during the Pro12 win over Zebre.
Wales back Liam Williams is set to return early in the new year following a foot injury which ended his World Cup.
Centre Scott Williams hopes to return from his World Cup-ending knee injury before the end of the season.
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"We had a lot [of injuries] last year and I thought that was quite a bit," Pivac added.
"But I'm learning very quickly that it seems to be commonplace.
"We do everything we can to give the guys breaks when they need them. If you don't listen to people's bodies you are going to get these injuries.
"We've got to be very careful with these guys. These guys have had a big workload and they are genuinely knocked around."
Scarlets host Glasgow in the return match on 19 December ahead of the Pro12 Christmas derbies against Ospreys and Cardiff Blues.
Pivac's side face Connacht at home on 10 January before they conclude their Champions Cup pool fixtures against Racing 92 and Northampton Saints.
"Hopefully we'll get through this week without any more [injuries]," Pivac added.
"What we've got to make sure is that we don't rush guys back too soon and end up putting them back another four or five weeks.
"It just shows the depth you have to have in your squads."
Head coach Wayne Pivac says Scarlets' current injury list is the worst he has faced since joining the region in 2014.