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."