Hibs and Dunfermline are locked on 19 points at the foot of the Scottish Premier League ahead of Wednesday night's two fixtures, with the Easter Road side away to Motherwell as their rivals play at Celtic Park.
Third-bottom Inverness are eight points ahead and have only lost to leaders Celtic in 2012 but Fenlon believes the relegation battle can be more than a two-horse race.
"We have been in a dogfight for a while," Fenlon said. "I still think we can drag one or two more into that.
"I think if ourselves or Dunfermline were able to win a couple of games on the bounce, it would bring other teams back into it. That's the challenge, to maybe pick up six points and see what happens.
"Once you get close to other teams, it starts to make them a bit edgy as well."
Fenlon tonight returns to the scene of what was meant to be his first match in charge of the club.
Hibs looked solid, committed and highly organised as they led Motherwell 1-0 at half-time in November but the match was abandoned because of a floodlight failure.
But that initial improvement has not been sustained consistently and Hibs now face a Motherwell side who have dramatically improved their home form, hitting 15 goals in four games at Fir Park.
Fenlon is not looking to match Motherwell's recent impressive form, he would be happy to stop them repeating it and scrape a win.
"Our job is to make sure that Hibs are playing against the Motherwells and the Celtics next season," the Irishman said.
"Whatever it takes to win football matches at this stage, I'm not really too fussed how we do it. Whether it's pretty or not good on the eye, I don't really care.
"We have got to just be determined to win football matches and get ourselves out of the situation we are in."
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