While explaining his strategy, Hodgson included the phrase 'feed the monkey', a reference to American space agency NASA sending monkeys to space.
"NASA decided they would finally send a man up in a capsule after sending only monkeys in the earlier missions," goes the space race joke.
"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'."
While Hodgson's words were meant as encouragement for Smalling to link up more with Townsend in the second half, one of the England players was reportedly upset with the racist connotations.
"I would like to apologise if any offence has been caused by what I said at half time," reads a statement from Hodgson.
"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."
Townsend himself is said to have taken no offence to Hodgson's joke.