The Selhurst Park outfit travelled to Vicarage Road without the Ivorian forward who picked up a hamstring injury following the M23 derby against Brighton and Hove Albion.
Michy Batshuayi's effort was not enough as goals from Etienne Capoue and Andre Gray ended Palace's sojourn in the competition.
After the defeat, Hodgson rued the unavailability of his talisman who has scored eight goals in 28 matches in all competitions this season.
"He [Zaha] is an outstanding player, when you take players of that quality in a team you're not going to be able to say you didn't miss them, you never know what sort of game they're going to have," Hodgson said, per SkySports.
"We don't really want to go into an important quarter-final without players of his ability and his importance. So that was a bit unfortunate as, of course, has been the Mamadou Sakho injury."
Zaha's injury comes as a blow for Cote d'Ivoire who have handed him a return to the national team for their final 2019 Africa Cup of Nations qualifying game against Rwanda after missing their last two qualifiers due to personal reasons and injury.
On whether the fleet-footed forward will be available for Crystal Palace's next outing after the international break, Hodgson said; "You never know with hamstring injuries and strains in the hamstring, you have to be very, very careful especially with players as explosive as Wilf. He felt it after the Brighton game and didn't train during the week.
"We took him out on Thursday just to test it slightly under control conditions but it was pretty obvious that it would have been an enormous risk to play him in the game today, a risk of much more serious injury. And with the two weeks now coming up, we can only hope he will recover in time when we play our next game."