Hamilton go into their Boxing Day clash with Kilmarnock on the back of one victory in nine matches since they triumphed at Rugby Park in September, their latest result a 4-0 defeat at Dundee.
But they have previously shown the ability to bounce back, after going 13 games without a win following the departure of Alex Neil to Norwich in January.
Hamilton finished last season strongly and started this season well, and could be back in the top six of the Ladbrokes Premiership by tonight.
Gillespie said: “Not that we are used to it, because you never like to be on a run like this, but the experiences of last season have probably helped.
“It’s obviously nowhere near as bad a run as that but it’s still not good.
“We know we need to get back to winning ways and there’s no better game to do it. Kilmarnock are on a run similar to ourselves so both teams will be determined to get three points.”
The 24-year-old added: “Our main objective at the start of the season is always to stay in the league and if we can do that we’ve had a good season. We are not in a crisis situation at the minute but we do know it’s vitally important to get back to winning ways.”