When asked about the 33-year-old, Hodgson said: "He's in good shape".
"He's a professional and committed to the club and helping us do what we need to do to stay in the league. Fans will react in the way they feel they should react", said Hodgson. "That situation has been and gone and Wilf will make certain he brings his straw to the water and help us have a good season, just like he has done in the previous two seasons".
Zaha was disappointed not to have moved away from Selhurst Park, after revealing his desire to leave at the end of last season.
Hodgson said: "They were a good team last season and they don't look like they're going to be any less good this year by the signings they have made".
Palace will be without James Tomkins (groin), Mamadou Sakho (knee) and Jeffrey Schlupp (ankle), but Hodgson is happy with his squad heading into the campaign.More news: Russia missile test blast kills five nuclear agency staff
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"It is unsafe at the start of the season when everybody is excited to talk about targets because so much depends on injuries", he said.
He subsequently handed in a transfer request after the bid was turned down, but a deal could still not happen between the two parties. "If we can be stronger there is no reason for us to have a lower total as our goal".
Zaha's introduction in the 63rd minute contributed to a Palace performance that became more convincing as the game progressed - and particularly when Everton's Morgan Schneiderlin was sent off after collecting a second yellow card for a foul Luka Milivojevic in the 76th minute.
The Sun is reporting that the Blues are keen on a move to bring the Ivory Coast worldwide to Stamford Bridge after he was heavily linked with a switch away from Selhurst Park in the summer window.
"If you listen to Marco Silva's press conference and read between the lines you'll see how unhappy he has been from what eventually transpired from a window in which Everton spent a lot of money, I have them at about £110m spending gross".