Yes! If I'd just been fired, the last thing I would care about are their feelings, and how my firing is part of the "strategic goal" I am no longer involved in.
He also mentioned taking full responsibility. That line should have been followed by how he did that. Pay reduction for himself? Upper management?
They don't really care what the people they're firing think as long as they aren't upset enough to sue or cause other problems.
Messaging like this is for the people who are still at the company. Talking about "strategic goals" is trying to reassure them that the company isn't on verge of collapse.
He also mentioned taking full responsibility. That line should have been followed by how he did that. Pay reduction for himself? Upper management?