Palace, still looking for their first Premier League win off 2022, make the trip to Vicarage Road to face Watford on Wednesday night.
Vieira took charge at Selhurst Park in the summer, as Hodgson left the club after four seasons in charge, and has since looked to transform Palace’s style of play.
Speaking at his pre-match press conference as he looked ahead to facing Hodgson’s Watford side, Vieira believes he has benefitted from the way the club was managed in previous years.
“Nobody will take away what Roy did at this football club,” Vieira said.
“He spent four years here and I think he did a fantastic job.
“I think the foundations of this football club are really solid and I think Roy was one of the people who put those in place to allow the next manager to come and to work.
“He brought stability to this football club and players with experience and that allowed myself to come to this football club and count on some of those players who know the club really well. That is what I think he left this football club.”
Watford have already had two clean sheets under their new manager, the only two they have managed in the league all season, and go into Wednesday’s clash high on confidence after a win at Villa Park over the weekend.
Vieira insisted Palace did not need to spring any shocks to counteract Hodgson’s knowledge of his former side, but revealed he has been impressed with the improvements the 74-year-old has already brought to the Hornets.
“I’m not surprised at all,” Vieira said.
“When you see the experience and how many years he’s been involved in the game, he knows what a team needs to get points and he’s doing a good job over there.”