The 29-year-old is free to negotiate with other clubs, having rejected the offer of a contract extension.
"If there is no further room for negotiation, I'm going to have to look elsewhere," Nicholson told BBC Sport. "It would have been nice to work things out. I have enjoyed my time, with last season ending on a high and playing in Europe this season."
"The manager has put together a good side and it's a great dressing room," added Nicholson.
"I understand the club's way of thinking but we're all really disappointed because we'd have liked to stay together and we all felt the club were going to work their hardest to keep us.
"It's been a great three seasons for me and there's still half a season to go.
"Obviously, I'll continue to do my best for the club and hopefully I can catch someone's eye."
When asked if he would like to follow Hart to England, the former Dunfermline star replied: "I've not really thought about it that much.
"When talks started it was all about staying with Aberdeen.
"It's something that always been at the back of my mind but I've got nothing concrete and it might not happen."