Defeat to West Ham United last Sunday has increased the need to claim all three points when Swansea City travel to Tyneside this Saturday or the gap to the top four could increase further.
The Magpies are already six points adrift of Everton in fourth after 11 matches and that is the target manager Alan Pardew has been aiming for having finished fifth last season.
But a failure to win at home for the fourth time in the Premier League this season this weekend would leave them outside the top ten ahead of back-to-back trips to Southampton and Stoke City.
Ameobi said: "We've been saying all season 'a win here will put us up there' and we said it last week against West Ham. Now it is the case for Swansea because losing that match puts a little bit more pressure on us.
"I think as players you thrive on that pressure a little bit. When the pressure was on last season we responded and hopefully we can do that again this time. We need to make sure we start off a lot better than we did last weekend and give ourselves a chance.
"If we get that lead, it breeds confidence and you play that bit better. We need to establish a better start in the game because, if we go behind, teams will sit back and defend like West Ham did and it can become a much more difficult game."
Despite winning just one from six league matches Ameobi feels now is not the time to start worrying too much about Newcastle's stuttering start to the campaign.
But Ameobi, who has been in Miami this week with Nigeria for last night's friendly with Venezuela, said: "We haven't been beaten that much but we haven't won that much either. "It's not the start we had last year but there's a long way to go and there's ability in this squad that saw us through this year. We're disappointed but we're not panicking. "There's a long way to go and there's a lot of improvement to do on our part. It's not as if we've been at the top of our game and losing games, we've got a little bit more to come and when that does come I'm confident that we'll be alright."
Newcastle's teenage striker Adam Campbell has been ruled out for two months with the knee injury sustained during a training ground match with Sunderland last month.