The Magpies drew 1-1 with the Portuguese giants at St James' Park on Thursday night following last week's 3-1 defeat forcing them out of the competition 4-2 on aggregate.
Ameobi, who set up Papiss Cisse's 71st minute opener, feels that having to beat Benfica by two clear goals was a little too much to claw back especially as Jorge Jesus' men had not been beaten in their past 31 outings.
"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," said Ameobi.
"That is the luck of the draw I guess but we gave it everything we got but two goals was a bridge too far."
He added: "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."