Tuesday's goalless draw with strugglers Peterborough leaves Boro six points adrift of the top six despite their recent four-game losing streak.
Ameobi, who joined from Newcastle back in February, says while it remains mathematically possible, they will keep fighting.
"It's not going to be easy," he told the club's official website. "What game in the Championship is easy? Everybody is beating everybody. The belief is still here, no one has given up.
"I think the gods have favoured us. We're still just six points away, we'll keep fighting and pushing. I don't know why results aren't coming. There are good players in that dressing room, good players who play good football.
"I understand the disappointment. But now we go to the other end of the table and Hull and look forward to another very competitive game."
Middlesbrough last week