The South London club finished 2015 with a 0-0 draw against Swansea City at Selhurst Park on Monday night which saw them remain fifth on the Premier League table.
Palace have amassed 31 points in 19 matches which is above the expectations of most, and although Ward is aware of the fact it is a fantastic result, there will be no resting on laurels as Palace look to push on.
"We would have taken 31 points at this stage at the start of season, but as a club we want to keep pushing on," he told the club's official website.
"We're on a great run at the moment and it would have been nice to get three points to give us a push up the league. But we'll take the positives and go into the New Year in high spirits and look to build on what we've done."
Ward also suggested Alan Pardew's side should have secured maximum points at home in what was a lacklustre performance against the Swans.
"The only thing that was missing from today was the goal because we had a lot of possession and managed to get in the final third enough times," he added.
"It was just the final ball that was letting us down and we couldn't find the back of the net."