The Hammers currently sit 12th in the table with seven games remaining after gaining promotion back into the Premier League through the npower Championship play-offs last season.
With former Bolton, Newcastle and Blackburn manager Sam Allardyce in charge and a host of experienced and international players amongst their ranks, a lack of big-game knowledge was never going to be the reason if West Ham were relegated.
O'Neil pointed to that collective experience, especially when compared to the likes of last season's Championship winners Reading who are now marooned at the foot of the Premier League, as well as a comfortable start to the season as invaluable.
"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 told Press Association Sport.
"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."
After a start that saw West Ham settle well into the top half of the table the Hammers stuttered during a spell after the turn of the year.
But recent victories over Stoke and West Brom, as well as a battling point at Liverpool on Sunday, mean any lingering doubt as to the Hammers' top-flight survival should now have been extinguished and O'Neil wants to finish the campaign strongly.
When asked if the team struggled to re-establish the form shown earlier in the season the former Portsmouth man replied: "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."
The 0-0 draw at Anfield at the weekend saw criticisms aimed at Allardyce's perceived negativity.
But O'Neil reckons every fixture has to be judged on its individual merits.
"It was one of those things," the 29-year-old added.
"We could have gone there and been slightly more attacking, you might come away with three points but the chances are they would have created more than they did. We restricted them really well to very few chances and no clear-cut ones at all really.
"We had Carlton Cole's chance and that was one of the best of the game, they had a lot of possession but chances-wise there wasn't too much in it."
Next up for West Ham is a trip to Southampton, also promoted last season, where a victory at St Mary's would see the Hammers leapfrog their hosts and, if other results fell kindly, could see Allardyce's side return to the top 10.