The midfielder, who joined the Cherries in the summer on a season-long loan, was not eligible to play against the Gunners in last Sunday's Premier League match, which ended 3-1 in Arsenal's favour.
Wilshere watched the action from the executive boxes alongside Arsenal striker Danny Welbeck, who is currently out of action with injury.
"It was really strange," Wilshere said in an interview with Sky Sports News. "I got to the game and walked up the tunnel and thought 'Where do I go first?' Do I go and talk to the Bournemouth boys? That felt right because they're my team at the moment.
"It wouldn't be right if I ignored all of them and went in and said hello to the Arsenal boys. Of course, I spoke to them after the game but it didn't feel right before the game. I said to one of the staff before the game 'I feel awkward here'. It was the same when I was watching the game.
"Danny Welbeck kept asking me 'Who do you want to win?' It was a strange one. I've never been in that situation before."
The 24-year-old, who joined Arsenal's academy in 2001 before making his debut seven years later, left the North London outfit on a temporary basis this summer in order to gain some first-team minutes following two years of injury woe.