Roy Hodgson insists Crystal Palace are looking upwards rather than over their shoulders following a 1-1 draw with West Ham.
Palace are just three points above the relegation zone but Hodgson insisted their display against the Hammers was not that of a struggling side.
"I did think our performance, particularly in the second half, was really good and it would have been a bit of a travesty to have got nothing," he said.
"Given the number of chances we had, the one goal we got was pretty poor reward for our efforts. The performance merited three points.
"We need to be able to play like this whoever we meet in the Premier League. That's what we're doing, and that gives me a lot of comfort.
"There are a lot of games to play. I can continue to hope these performances can get us into the top half of the table.
"My perception is that I think I've got a very good football team and they showed it today.
"I'm entitled to have faith in this team and believe that they should be less concerned about the teams below them."
Noble had fired West Ham into a 27th-minute lead after Palace keeper Vicente Guaita clattered into Michail Antonio.
Palace would have equalised earlier but for an incredible miss by James McArthur, who somehow fired wide from four yards out.
Instead it was Zaha, sent off at Southampton last week for sarcastically clapping the referee, who milked the applause with his 76th-minute leveller, an angled drive which clipped the boot of Issa Diop.
Hammers boss Manuel Pellegrini felt a draw was a fair result, even though they were clinging on at the end.
"It's a good point because I think it was 45 minutes for each team," said Pellegrini.
"We had chances in the first half and Palace didn't have too many opportunities, but in the second half they didn't have any problems in their box.
"They scored a lucky goal, it was a deflection, but they dominated the second 45 minutes.
"Crystal Palace is not an easy team, so I'm not disappointed. You always want to win but a draw was a fair result."