Sam Allardyce's side were only promoted to the top-flight last season but they lie 12th in the table, six points clear of the relegation zone.
O'Neil is convinced the experience in the camp has aided their cause following their return to the Premier League via the play-offs last season after they were relegated in 2010/11.
"We maybe had the edge because we have got a lot of players and the manager and staff who have played and worked in the Premier League before," he said.
"We were only down for a season as well so the lads are used to playing in the PL so we maybe took to it quicker than they did.
"We also we had a slightly easier run of fixtures at the start that helped us build up some momentum."
Following a strong start to the season that saw that saw the Hammers settle into the top half of the table they began to struggle after the turn of the year.
But recent victories over Stoke and West Brom, as well as a battling point at Liverpool on Sunday, have left Allardyce's side in a strong position to play top-flight football next season.
When asked if the team struggled to rediscover their early season form, O'Neil added: "I think it took us a little while, it does hit you confidence-wise as a squad.
"Even if you are losing to the likes of Chelsea and Manchester United, it does dent the confidence. It was hard to get another run going.
"But fortunately we've got a little one going now and have picked up seven points from our last four games which is good and can hopefully be added to this weekend.
"We've always said we want to finish as high as we can, we weren't just focusing on avoiding relegation.
"Our aim was always to finish as high up as possible, we want to get to 40 (points) first to make well and truly sure we are safe but then by no means will we stop there."