The Republic were looking to build upon their first win under O’Shea, a 2-1 friendly victory against Hungary at Aviva Stadium last week.
It was a much tougher ask for O’Shea’s side in Aveiro, however, with Portugal looking dangerous during the early exchanges.
Joao Cancelo fashioned an opportunity from left wing-back on nine minutes, finding Rafael Leao, who cushioned the ball back to Felix, with his shot blocked by Liam Scales.
Leao then slipped in Manchester United captain Bruno Fernandes and he weaved past a diving Caoimhin Kelleher before seeing his shot from a tight angle blocked by Jake O’Brien.
Kelleher was called into action on 17 minutes after a slick Portugal move, which started and ended with Fernandes.
He fed Ronaldo, who found the run of Diogo Dalot, and despite being in a favourable position in the box the wing-back opted to pull it back to Felix, whose first-time low strike was turned behind by the foot of Kelleher.