Tuesday's defeat at the hands of Carlisle United continued the club's search for a recent win following a run of eight draws and five losses from their last thirteen games.
Jones accepts City's current form isn't encouraging but he also knows that Parkinson's men can't run and hide if they want to turn their results around.
On the eve of the club's trip to Coventry City this weekend, Jones has called on all parties with City close to their hearts to form a united front to help the Bantams back up the table again.
Jones said: "It has been a difficult period for everyone but what are you going to do? Are you going to sink or are you going to swim?
"Sometimes you get tough times in football and the only way to get through them is to stick together.
"Football is a funny game, full of high and lows. Now is the time that we have to work harder than ever though.
"As I say, it is vital we stick together as a club. That includes players, staff and, most importantly, the fans.
"They played a major part in our success last season and they have big role to play now, especially with three home matches on the trot on the horizon after the Coventry game.
"We know that the fans will back us all the way though, we have no doubts about that, it is important that we show them what it means to wear the Bradford City shirt.
"It should mean everything to the players.
"We know now is the time to roll up our sleeves, wear our hearts on our sleeves and show people what we're all about.
"If we do that, we are confident that the results will turn around sooner rather than later."