Zaha handed in a transfer request before the window closed but Palace refused to budge on their reported £100 million ($121 million) asking price and rebuffed Everton's interest.
The Ivory Coast international will get a taste of what might have been when Marco Silva's men visit Selhurst Park on Saturday.
After sending him home from training on deadline day, Hodgson said Zaha is "absolutely" in contention for the club's first Premier League fixture of the new season.
"Wilfried Zaha is as I expected he would be," the Eagles manager told reporters on Friday.
"He's a professional and committed to the club and helping us do what we need to do to stay in the league.
"He trained today just as he did on Tuesday and Wednesday.
"I can't say he's jubilant or delighted. The outcome he wanted was to be sold and leave, but it was the last thing we wanted. It was a good outcome for us.
"It's not even worth discussing replacements for players of his calibre."
Zaha, 26, was heavily linked to Arsenal before the Gunners opted to sign fellow Ivory Coast attacker Nicolas Pepe to bolster their front line.
Everton emerged as contenders for his signature next, but the move was rebuffed in the final days of the transfer window.
Having come up with Crystal Palace as a youth player, Zaha originally featured for the club in the Championship from 2009-13 before sealing a transfer to Manchester United.
He managed just four total appearances at Old Trafford and rejoined Palace from Manchester United on loan in 2014 before making the move permanent a year later.
Zaha scored 35 goals in 180 appearances for the club, including 10 goals in all competitions last season with all 10 of those goals coming in the Premier League.
The winger could still leave south London if a club elsewhere in Europe successfully agrees a fee with Palace.
Palace will face Everton on Saturday in the club's first match of the campaign before visiting Sheffield United and Manchester United in their next two matches.