Greenwood, 21, had been facing charges including attempted rape and assault but the Crown Prosecution Service said the case had been discontinued as "the withdrawal of key witnesses and new material that came to light meant there was no longer a realistic prospect of conviction".
On Friday Ten Hag declined to comment on Greenwood's case directly, instead referring to a United statement which said "the club will now conduct its own process before determining next steps" regarding the academy product, who has been suspended from playing and training since January 2022.
Ten Hag has worked hard to change the culture at United since he arrived in the summer, removing distractions and instilling greater discipline, and he is determined to maintain the same approach.
"It's really important but sometimes you get issues," he said. "Then as a club and team you have to deal with it. We have standards and values. We have to live along those high standards and values and that gives a base if you have a good culture and spirit."
Ten Hag was able to remove one big distraction with the exit of the unhappy Cristiano Ronaldo last year, and United's form since the World Cup - 10 wins from 12 matches - offers its own verdict on how the team has responded.
"That's our job, not to get distracted by anything," Ten Hag added. "We are human beings and sometimes there are issues, we are not like robots, but we have to focus on our job.
"We have so many games so we don't have time to get distracted by anything. It's not easy but that is our job."
United used Tuesday's transfer deadline day to bring in Bayern Munich midfielder Marcel Sabitzer on loan - providing cover following long-term injuries to Christian Eriksen and Donny van de Beek, as well as a shorter-term issue for Scott McTominay.
Sabitzer followed loan deals for Burnley striker Wout Weghorst and Palace goalkeeper Jack Butland, ineligible for Saturday's match against his parent club, as United used the window to address short-term problems.
It was a relatively conservative approach compared to some of United's rivals in the battle for top-four places, but Ten Hag believes he has the required depth in his squad.
"We construct a squad and also invested in the summer," he said. "From that point on it's about developing a team and that has to come on the training ground and come in the matches that you develop your team…
"Of course we need players to cover that because there is a limit on every player but I think we have a depth in our squad. Maybe not that far as other teams but that also has something to do with your approach to it and how you do your load management. If you do that right, I think we can go far."
When it comes to load management, injuries in midfield mean there is little prospect of a rest for Casemiro, who has started 21 of United's last 24 matches and only missed one entirely when he was suspended for the trip to Arsenal.
Asked if there was a risk of burn out, Ten Hag said: "It is (a risk) for every player and Bruno (Fernandes) is also playing every game.
"Those players are capable of it and that's why they are so good. You can always rely on them as a club and that's why they have won so many trophies."