Wanderers are six points clear of the bottom three with nine games to play and look well placed to avoid the drop, although Parkinson is well aware they have plenty of work ahead of them if they are to retain their Championship status.
“I honestly don’t feel we are ‘nearly there’ and I think the minute I do think that will be the moment we get dragged right back into it,” Parkinson told the Bolton News. “We have only achieved something if by the end of the season we’re above that dotted line.
“Right now, I think we have a lot of work left to do. There are some really good elements of our play, we’re controlling the game a lot better over the last two away games.
“So I am happy we have started to evolve a little bit, I am pleased with the results we have got away from home, but I am not getting ahead of myself. We are still in a dogfight.”
New Walsall manager Dean Keates will be in charge for the first time when promotion-chasing Wigan visit the Banks's Stadium on Wednesday night.
Rochdale have no new injury worries ahead of Tuesday's Sky Bet League One relegation battle with fellow strugglers Fleetwood.
Northampton striker Kevin van Veen is hoping to make his first start in over a month in the home game against Shrewsbury.