Fenlon's future became the subject of speculation after his side lost 7-0 at home to Malmo in the Europa League last week following a 2-0 loss in Sweden.
The Irishman has led Hibs to two William Hill Scottish Cup finals in less than two years in the job but both ended in emphatic defeats and Fenlon himself declared last season a failure because his team were unable to secure a top-six finish.
With Hibernian's second Scottish Premiership game coming against the youthful team of administration-hit Hearts across the city, Fenlon is eager to get off to a good start against Motherwell on Sunday and begin to put their Europa League embarrassment behind them.
But there is no let-up in the pressure as Hibs will be without most of his first-choice back four when Motherwell visit Easter Road.
Fenlon appreciates he is under intense scrutiny following the nature of the European exit but he wants the supporters to back the team despite their frustration.
"It will put extra pressure on me, hopefully, rather than the team," he told Press Association Sport.
"The team have just got to go out there and play football and hopefully get a decent result.
"It's like everything in football, if you get two or three decent results then people tend to move on pretty quickly."
Fenlon refused to dwell on his own difficulties following last week's defeat, the highest aggregate loss suffered by a Scottish team in Europe.
"It's football at the end of the day," the 44-year-old said. "I have faced difficult times outside of football as a person never mind as a manager, so you have to get on with it.
"It's part and parcel of the game. If you're a manager in the firing line you have to accept it. If you don't want to do that then don't be involved in it."
And, while learning from what went wrong against the Swedish side, Fenlon has tried to look forward this week.
"We have got to learn from our mistakes as a manager and players, you have to learn from when things go wrong," he said.
"I have looked at it and obviously feel there are things we need to adjust, but it's a completely different game and we have got to make sure we are ready for that.
"That's what you get paid for as a manager when you have poor results, to make sure the players are lifted and ready for the next game.
"That's what we have tried to do this week. We have a tough start to the league but it's really important to get off to a good start."
Hibernian's difficult opener against last season's runners-up comes on the back of a selection crisis.
Captain James McPake is still out with the back injury that forced him to miss the end of last season and go off against Malmo when the score was only 1-0.
Fellow defenders Tim Clancy, Ryan McGivern, Bradley Donaldson and the suspended Jordon Forster are also missing.
Striker Rowan Vine is suspended while midfielder Paul Cairney faces up to three months out with ankle ligament damage sustained in training last week.
Fenlon has had one piece of good news on the injury front with midfielder Owain Tudur Jones back from the knock that meant he missed the thrashing by Malmo, while forward James Collins is in line for his debut after completing his move from Swindon.