Sean Holley has warned the Scarlets of an Ospreys European backlash after his team suffered potentially damaging back-to-back Heineken Cup defeats.
Ospreys' quarter-final chances are slim as their one Pool Five win means they face not making the knockout stages of Europe for successive seasons.
Ospreys gave their players a "few days off" to "lick their wounds" ahead of the festive Pro 12 derby period.
"We'll come out fighting over Christmas as we're hurting," said coach Holley.
Saracens inflicted a double blow on Ospreys' European hopes as the English champions followed up their victory at Wembley by being the first visiting team to win a European game at the Liberty Stadium for six years.
Holley, though, has challenged his Welsh region to respond positively over the festive period and maintain their Pro 12 title pursuit, as the second-placed Ospreys are just a point behind leaders Munster.
Ospreys travel to Scarlets on Boxing Day, then host the Cardiff Blues on New Year's Day before visiting the Newport Gwent Dragons on Friday, 6 January.
"Saracens haven't done those teams any favours by beating us," said head coach Holley.
"We're hurting and that's a dangerous thing for an opposition."
"We have the toughest draw with three games in 12 days and two away from home, but that's the way we like it.
"The derby games give us different motivation, we've had a lot of away wins and we want to keep that momentum going."
Ospreys have lost just once this season in the Pro12 and are unbeaten in seven matches against their west Wales rivals.
"We're up there and the derbies over Christmas are an exciting time," added Holley. "They mean a lot to the players.
"It's time for us to bounce back these next couple of games over Christmas."
Ospreys' 60-17 win over the Scarlets last December is the second biggest win in their history and the Llanelli-based region's worst league defeat since the inception of regional rugby.