Armstrong is currently on loan with the Sky Blues, and he has made a fine start to the season, netting six times in his first seven League One matches.
With Newcastle struggling for goals, there has been a growing clamour for them to utilise their 24-hour recall clause in the striker's loan deal and give him a chance in their own first-team.
However, Mowbray thinks that this would be a bad idea, as it could potentially demoralise the new additions to Newcastle's squad.
“I suppose Steve has to look at it and be conscious that you have got to give a £15million striker time to settle in," he said. "I know he got himself sent off but, like with some of our young players, you give them time to see who their friends are, who they can trust, how they fit into the group really. They need time to settle in and it can be harder if they’ve come from another country.
“If you are going to stick those players on the bench and play an 18-year-old kid then you’re going to demoralise them because at that money they come with an ego and think they’re going to score goals in the Premier League. It’s their dream then, all of a sudden, an 18-year-old boy sits them on the bench. You have to be careful how you manage the personality of those players."
Mowbray's analysis of the situation may be protecting his own interests, as Armstrong has been key to his side's efforts so far.
Coventry have made a bright start to the new campaign, and with Armstrong up front they have one of the most lethal strikers in the division in their ranks.
At the moment, the 18-year-old's loan deal lasts until January, when both sides will have to review the situation before deciding whether or not to extend the temporary move through until the end of the season.