The Chelsea star scored two goals in the Three Lions' 5-0 win in Chisinau in their opening game of the 2014 World Cup qualifying campaign.
"Frank was excellent," The Guardian quotes Hodgson as saying. "Like Steven [Gerrard], he is a quality player, and quality is permanent.
"That's been proved time and time again. They might not always play at the very top of their game, but you're always better off going into games with that quality on the field."
England are back in action on Tuesday when they host Ukraine at London's Wembley Stadium in their second Group H fixture.