The England international, on loan from Atalanta, struggled against Son Heung-min and was subbed at half-time after receiving a booking.
McKenna explained that keeping Godfrey on wasn’t an option, citing Axel Tuanzebe’s red card at Aston Villa the previous week as a cautionary example.
“I think with a yellow card it wasn't very difficult because he's up against a really good opponent,” McKenna said.
“And the yellow card at half-time would have made it dangerous, especially for the feeling of the team after what happened last week with Axel, so the yellow card meant it wasn't a particularly difficult decision to make.
“He's trained well today. He's trying to give good things to the group. He's come in with a really good attitude today and has trained well and we're going to need him across the games to the end of the season.
“Saturday was a challenge, but he's a strong character and he's fitting in really well with the group. He's shown in his attitude today and since he's been here, he really wants to help the team.”