The Republic of Ireland international came close to signing for Steve Bruce's side in the final moments of the transfer window before the move fell through amid much finger-pointing from both clubs but the defender has been impressed by the way in which the former Reading striker has negotiated the potentially awkward situation.
"I think Shane has coped with it well," Olsson told the Birmingham Mail. "It's just part of football; you have been in some transfer windows, one day you are going, next you are staying, it's part of it.
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"I think he's shown against Arsenal [in the 1-1 draw on October 6] that his head is still here, so we're not worried about him."
Olsson believes that a bigger squad and increased competition could help improve performances on the pitch and is therefore pleased to see the striker still around.
"I'm happy we managed to keep him," he continued. "We have competition all around now; it will do the squad good.
"Competition is vital for a team to progress and develop. It is vital for such a long season to have not only 11 players but 20 to 25 players and that is what we were lacking a bit, maybe, the last part of last season. Now we have greater depth."