The Magpies are currently eighth in the Premier League after losing just two of their last 10 outings and Nigerian striker Ameobi insists they have a strong platform to build from.
Alan Pardew's men fell to their first defeat in five on Sunday as Olivier Giroud headed Arsenal to the summit as the first half of the season reached a climax.
Defeat at St James' Park at the weekend ended a four-match unbeaten run for Newcastle, which began at Old Trafford on December 7 when Yohan Cabaye saw the visitors to a 1-0 victory over defending champions Manchester United.
Newcastle also beat title contenders Chelsea and big-spending Tottenham earlier in the season, as well as earning a 2-2 draw against Liverpool, and Ameobi believes their position reflects the progress made in 2013.
"Our confidence is sky high at the moment and that's probably highlighted by the fact we were disappointed not to have got something from the Arsenal game," he told The Sun.
"We're going into 2014 thinking we can achieve something special and that's pretty incredible when you look at where we were 12 months ago.
"It's great to have a squad that's together and wants to get better."
After battling against relegation last term, eventually finishing 16th, Ameobi insists Newcastle have the credentials to stake a claim for a top six spot and place in Europe.
"It's going to be tough to finish in the top four, five or six but we'll give it a go," he added.
Newcastle will aim to return to winning ways on New Year's Day when they visit The Hawthorns to face a managerless West Bromwich Albion side.