The Hammers are currently eighth in the table with three wins and two draws from their opening seven matches.
"We have made a good start and want to get better as the season goes on," O'Neil told the club's official website. "We have had good results in the first few weeks and started to build the foundations of what we want to achieve.
"There is a really good vibe around the place. The lads have done fantastically so far this season. We have had a decent start and coming up from the Championship is hard, so getting a good beginning to the campaign is important."
West Ham resume their Premier League duties when they entertain Southampton at Upton Park on October 20.