Villa have finished sixth for the past three seasons but a lengthy injury list has left them in mid-table - five points off the top five but also just three points off the relegation zone.
Dunne believes the next few weeks will be crucial in defining which way Villa's season will go after collecting 10 points from nine games under new manager Gerard Houllier.
The Republic of Ireland international said: "Between now and the end of January, it is important to pick up points because the league will start to spread itself out.
"We want to make sure we are in the higher half of the table and we can then push on to hopefully make another top six or seven finish. But, once you get on a run of defeats, it's really difficult to get out.
"Against Arsenal, we need to put in the same performance as against Manchester United."