On New Year's Day, the Hammers were second from bottom in the Premier League table and three points from safety.
But by May, they had moved six places up the standings to 13th to finish seven points clear of the relegation zone.
Starting with a goalless draw against Chelsea on January 29, Sam Allardyce's side went on a run of six wins and one draw in 10 games to secure their Premier League status for another season.
And Noble admitted: "It was a tight league and a couple of results can push you up the table.
"We managed to win four in February, then beat Hull at home and Sunderland away to confirm our safety.
"To beat Spurs in the last home game of the season finished it off nicely.
"It has been tough but we have finished 13th and we were second from bottom in December.
"It is a credit to the lads and everyone involved in the club that we got ourselves out of that and ended up 13th."