The Hammers were beaten 2-0 by Everton at the weekend, a game which marked David Moyes' farewell to the Goodison Park faithful ahead of his move to Manchester United.
But O'Neil is keen for West Ham to sign off their campaign with a win at Upton Park on Sunday to cap an encouraging return to the top flight following promotion last season.
"We need to do some work this week and make sure we finish the season on a high against Reading," he told the club's official website.
"The aim from the start has been to finish in the top ten and the fact we're safe already had no part to play in our performance on Sunday.
"It was just a poor performance all round. That's gone now, we'll have a look at it, see where we went wrong and make sure we're ready for Reading.
"We've done enough to justify being around the top ten so if we can produce a big performance this Sunday we can get there."
O'Neil, signed from Middlesbrough in January 2011, has played 27 times for Sam Allardyce's side this season and is delighted to have been part of his plans.
"I've enjoyed the run of starts, Sunday was the 11th on the trot - I've enjoyed all of my time here," he added.
"The lads are all great and in the two-and-a-half years, I've enjoyed being around the squad, even when I haven't played.
"The fans have been brilliant, and for the two full seasons I've been here, we've had a promotion and a good season in the Premier League, so it has been successful."