The 26-year-old winger handed in a transfer request a day before the Premier League transfer window closed, Sky Sports News understands.
Hodgson says Palace were prepared to allow Zaha to leave but Arsenal and Everton failed to meet the Ivory Coast international’s £80m valuation.
Zaha, who has come through from the academy, has since played in all four of Palace’s Premier League matches so far this season and has settled any previous discontent with the club’s hierarchy over the transfer saga.
“With Wilf, I don’t think anyone was thinking we definitely must block him because we want our best player still with us,” Hodgson said.
“We understood that if a really big offer comes his way and a much bigger club than Crystal Palace want him, and he is desperate to go, we are going to have to try and do some kind of deal.
“The unfortunate thing for Wilf is that offer did not come his way from the sort of club that he would want. I think Steve Parish has made that clear to Wilf and they’ve thrashed that side of it out.
“As a result it is not a major problem for me with Wilf coming back, having accepted the situation. The way he works here is just the same as it was. Since the first day he has been mature about it.”
Zaha would have been the second high-profile departure at the Eagles in the summer had he left Selhurst Park, after Aaron Wan-Bissaka joined Manchester United for £50m.