Hodgson implored right-back Chris Smalling to "feed the monkey" - referring to Townsend and the NASA joke - in a bid to capitalise on England's 1-0 lead at the interval.
Townsend, who scored on his debut against Montenegro four days previously, had hit the crossbar in the first period and was causing Poland problems on the right wing.
Hodgson praised Townsend after both qualifying wins
However, Hodgson clarified his comments last night after one England player leaked his remark, much to Townsend's insouciance.
"I don't know what all this fuss is about," Townsend said on Twitter. "No offence was meant and none was taken! It's not even news worthy!"
England forward Wayne Rooney has also expressed his support for Hodgson, labelling the story "ridiculous" and claiming "he's done nothing wrong".
Hodgson's advice for Townsend stems from a popular Nasa joke about sending a monkey into space.
The joke goes:
"Nasa decided they’d finally send a man up in a capsule after sending only monkeys in the earlier missions.
"They fire the man and the monkey into space. The intercom crackles, 'Monkey, fire the retros’. A little later, 'Monkey, check the solid fuel supply’.
"Later still, 'Monkey, check the life support systems for the man’. The astronaut takes umbrage and radios Nasa, 'When do I get to do something?’
"Nasa replies, 'In 15 minutes – feed the monkey’."
Townsend linked up with Smalling during England's win over Poland
Hodgson, mortified at how his observation was interpreted, apologised on Wednesday night.
"I would like to apologise if any offence has been caused by what I said at half-time," Hodgson said. "There was absolutely no intention on my part to say anything inappropriate. I made this clear straight away to Andros in the dressing room.
"I also spoke to Andros again on Wednesday. He has assured me and the FA he did not take any offence, and understood the point I was making in the manner I intended."