The Irishman has struggled to win over some of the faithful since taking over from Colin Calderwood two years ago, a club-record 9-0 defeat to Malmo in a Europa League qualifier intensifying the pressure.
However, a recent six-match unbeaten run - which was ended by Inverness at the weekend - has brought some stability, and Fenlon is sticking to his principles.
He told the Evening News: "I know where we are at the moment is not good enough but from where I came in to where we are now, I feel we have made progress.
"I will do as much as I can to turn it around. If it does not happen, I won't stay around to see failure.
"I know things have been difficult, the start of the season was a disaster and that's down to me as manager, no-one else.
"It's up to me to win football matches. If I don't do that, I won't be here and I won't need anyone to tell me I haven't done my job."
Fenlon is adamant that, having made 10 signings over the summer, there will be much more to come from the present squad.
"I do not think we have been as good as we can be. We have a lot of new players and it takes time to settle and gel," he said.
"We also have to chop and change because of injuries but I think there are signs it's improving.
"Confidence is a big thing and you do see the lift the players get when they know the crowd is with them.
"I believe the club is going in the right direction but I guarantee if I cannot do that, I will not hang around."