Alan Pardew's side are currently ninth in the Premier League, eight points adrift of Everton in sixth, which looks set to earn a spot in next season's UEFA Europa League.
Ameobi insists he and his team-mates still harbour hopes of a productive end to the campaign.
"Hopefully I can help us in these last nine games and play a part in the run-in," the striker told The Journal.
"Hopefully we can finish in a European position, which is our ambition as a club.
"We still believe we can do it. As players you look and see there is still 27 points to play for.
"That's a lot of points and way more than enough to get us into Europe.
"We're still fighting even though Southampton have gone ahead of us (into eighth) but we play the next two games at home and they will be vital come the end of the season as to where we finish."
Newcastle suffered a surprise 1-0 defeat at Fulham last weekend, but with fixtures against teams around them still to come, Ameobi knows a good run of form between now and the end of the season could see them make a late charge.
"We've got Everton, Manchester United and Southampton," he said. "Whatever happens in those games will probably determine how well we do, but every game is huge now.
"It's important you continue to carry the momentum we've had throughout the season.
"We don't want the season to peter out, we really want to push ourselves as players."
