The Mali international levelled proceedings for the Eagles - with a superb 25-yard strike - after they went down to Brighton and Hove Albion in the first half. But a late goal from Glenn Murray ended their campaign in the competition.
The winger has been impressive playing as a striker and has scored three of his five goals from that position this season.
But he has found regular playing time hard to come by with Christian Benteke and Wilfried Zaha ahead of him in the pecking order.
The English tactician is, however, confident that the former Wolverhampton Wanderers player has proven that he deserved a starting place in the squad.
“He’s proven that he’s capable of a regular starting place,” Hodgson told club website.
“He faces competition from Benteke and Zaha but it’s good to know that he’s there as well. We’re going to need him; our squad is so unbelievably thin and it’s been thinned even more.”
Sako will be eyeing a starting place when Palace welcome Burnley to Selhurst Park for their next English Premier League encounter on January 13.