Central defender Smalling was sent off in the first half for two bookable offences as Manchester United went down 1-0 to rivals City at the beginning of November.
Having been booked for a tangle with Joe Hart, Smalling lunged in recklessly on James Milner to pick up a second yellow card, prompting United boss Louis van Gaal to label the dismissal "stupid".
However, Smalling is looking to move on and revealed Hodgson had not spent much time discussing the topic during the international break.
"I really respect Roy. He gave me my chance at Fulham. I was nowhere and he plucked me out and gave me that chance," said Smalling, who started as England beat Scotland 3-1 in Glasgow on Tuesday.
"He didn't need to say much about the sending off because it was very out of character for me and I just have to move on.
"The red card was disappointing but I rarely get yellows so hopefully it will never happen again."
Smalling earned his 15th England cap against Scotland and will hope to feature when United take on Arsenal in the Premier League on Saturday.
