"I don't underestimate the challenge but I have been heartened today that I've found a willingness to listen," she said in Brussels six days after Britain -- but not Scotland -- voted to leave the EU.
She said after meeting European Commission president Jean-Claude Juncker and MEPs that she had met "a lot of people expressing support for Scotland's position and wishing good luck in its attempts to protect its position with the EU".
"But I leave Brussels tonight in good heart and optimistic," she told a news conference.
While Britain as a whole voted 52-48 percent to leave the EU, Scotland voted 62-38 percent to remain.
Also Read
Scots rejected independence in 2014 but since the June 23 Brexit vote, there have been calls for another referendum to give Scotland the option to remain in the EU.
However, even assuming that such a referendum is held -- which Prime Minister David Cameron opposes -- and returns a result in favour of breaking the centuries-old union, acquiring EU membership is far from guaranteed.