It was always going to be an uphill battle for the North-East club, who lost 3-1 in the first leg in Lisbon, but they gave themselves hope when Papiss Cisse scored a 71st-minute header, his fifth goal in seven games.
However, as they were pushing for another goal - which would have seen them into the semi-final - Eduardo Salvio struck deep into injury time to send the Portuguese side through with a 1-1 draw and a 4-2 aggregate win.
Ameobi admitted the damage had been done in the first leg and said: "Two goals is a lot to come back but tonight we gave it a right good go. We knew with our fans we would have a good chance.
"That is the luck of the draw I guess but we gave it everything we got but two goals was a bridge too far."
Neither did Ameobi agree Newcastle were not attacking enough in the early stages of the game.
He said: "We knew they were a good side, we didn't want to concede early on.
"We had to be cautious but we had to take it to them.
"We made the substitutions and went for it but got caught with a sucker punch there.
"Credit has to go to the lads - getting to the quarter finals of a big competition is something special."