The Leith manager is facing mounting criticism following the club's dire start to the season - with fans already calling for the Irishman to be replaced.
The Edinburgh side suffered Scotland's worst ever European result when they were humiliated 7-0 by Malmo in the Europa League qualifiers before losing to Motherwell in the Scottish Premiership opener.
To make matters even worse, Fenlon's side then lost 1-0 to administration-hit Hearts in last Sunday's Edinburgh derby.
Popular supporters forum Hibs.net even asked fans in an online survey if the 44-year-old should stay or go following the Tynecastle defeat, and around 93 per cent of the near 600 respondents indicated a change was now needed.
But Fenlon told Press Association Sport: "I bump into supporters now and again. I don't have too many conversations with them to be honest, just because I'm too engrossed in the job that I'm not around the town very often.
"But the supporters have been different class and we just ask them to continue to do that. They have backed the team to the hilt and there is nothing negative from me in relation to that. They have been brilliant."
Despite the flak being directed his way, former Bohemians and Shelbourne boss Fenlon put a brave face on as he defended his side's record so far this season.
The club have lost all four matches, conceding 11 goals while failing to score at all at the other end.
Since replacing former Easter Road boss Colin Calderwood, Fenlon has seen Hibs lose 45 per cent of the league games he has been in the dugout for.
For many of the club's supporters, Sunday's derby defeat was the final straw and the boss was treated to a chorus of angry boos following the match won by Callum Paterson's second-half header.
But Fenlon insists his players have responded in positive fashion, claiming: "It hasn't been hard picking the boys up. I have to be honest and say it has been a good week.
"It's not been doom and gloom at the training centre. The players have certainly been bubbly and trained really well.
"The crux of the matter has been the European result, which was so poor.
"But the league games, we have lost both of them when in my eyes we should have got something out of both of them.
"That's football, it's the way the game has gone. You are only ever two games away from a crisis, no matter what club you are at. You have to deal with it.
"But the players have been brilliant and are looking forward to the weekend."
The one consolation Fenlon can look upon ahead of this weekend's meeting with Dundee United is that Jackie McNamara's side have hardly started the new campaign on fire either, following up their goalless draw with Partick a fortnight ago with a 1-0 defeat to Inverness.
"They are a lot like ourselves in that they have made a lot of changes and are trying to gel it together," said Fenlon.
"But they have got some really good players in Gary Mackay-Stevens and David Goodwillie and experience dotted around their team too. We will need to be careful."
Fenlon had hoped to give his team a boost by capturing former Celtic winger Paddy McCourt but the Northern Irishman is still hoping to land a move to America.
The Hibs boss, however, does have a plan B if McCourt cannot be persuaded to move to the capital.
"There's nothing new on the situation with Paddy," Fenlon said. "We would love to be able to sign him. He's a very, very good player and will have a lot of options.
"We are doing as much as we can to make that happen. We want to bring in a wide player if we can and Paddy fits the bill. But there are one or two others that we have had a look at in case it doesn't happen."