Zamora, pinpointed last week by Hodgson as just the kind of player England will need at the World Cup, struck twice just before the interval and ran the Basel defence ragged. The much-maligned striker has now scored four in his last three games and nine this season to answer his critics.
"Bobby Zamora carried on from where he left off in the Premier League,'' he said. "I thought he was very unlucky to have a first goal ruled out for offside, and he was a real thorn in the flesh of the Basel defence.
"I took him off as a precaution, he had a slight problem with his back. But he's got to be delighted with his performance. Bobby is one of our more popular players, he has a chant of his own and the fans seem to appreciate and like him.
"The one criticism is he hasn't scored enough goals but nine goals is a pretty good return for any forward. We were pretty good value tonight for the goals we scored and we could have scored more.''
The draw for the first knockout round is on Friday and, although Fulham cannot draw Liverpool, they could be paired with the likes of Juventus or Atletico Madrid who also dropped out of the Champions League.
Hodgson has consistently prioritised the Barclays Premier League ahead of Europe and he started tonight with Brede Hangeland, Clint Dempsey and Damien Duff on the bench in preparation for Saturday's clash with Manchester United.
"I don't know whether I am enthusiastic (now we have qualified), I am very satisfied. I am particularly pleased for the fans,'' Hodgson said. "I walked around Basel today and I was stopped by fans saying how much they were enjoying the adventure. I am looking forward to the next round, the draw to see who we get and then we see how far we can go.
"I wouldn't mind playing Juventus. We have done more than we set out to do. It's been a bonus so far and now we face an even bigger bonus.''