Zaha played a crucial role in Palace's 3-2 win at Arsenal on Sunday, capping a fine performance by scoring the Eagles' second goal.
The display came on the back of suggestions by the Ivory Coast international, who penned a new contract at Selhurst Park in August, that he may be forced to leave Palace in order to further his career and test himself at a higher level.
Paris Saint-Germain and Borussia Dortmund are among the clubs to have been linked with the former Manchester United forward, but Hodgson, despite not pinning blame on Zaha for responding to questions about his future, is adamant Palace will fight to keep their star player.
"When the journalists pose a question about playing at a higher level, I don't know how you're supposed to answer," Hodgson told BBC Sport when asked about Zaha's interview with the Daily Mail.
"Sometimes journalists force you into those questions. In football, you have to be prepared with what life throws up.
"We don't want Zaha to go. We can't stop players from doing those interviews, but he's done it and said what he said. He signed a long-term contract with Palace and we will do our level best to hang on to him.
"We have no interest and desire in selling Zaha. If he plays like he has done, then it bodes well for the rest of the games and the future."
For his part, Zaha is remaining focused on rounding off the season in style with Palace, who face Everton next time out.
"To be honest the only thing I'm thinking about is Palace. I'm a Palace player right now and I don't know what the future holds for me," Zaha told Sky Sports.
"I'm here at Palace, working for Palace. I'm not being distracted by anything else."