The Easter Road chief met with an angry supporters group following the club's awful start to the season.
Hibs suffered Scotland's worst ever European result when they were thumped 9-0 in the Europa League qualifiers by Malmo.
Fenlon's side then suffered further humiliation by losing to city rivals Hearts as they opened the season with four straight defeats.
In a statement released through the club's website, a spokesman said: "Hibernian chairman Rod Petrie met with supporters this evening. The meeting was arranged to allow supporters from throughout the Hibernian community to speak directly with the club about any issues.
"Supporters were understandably critical of performances and results, particularly against Malmo at home and at Tynecastle in the Edinburgh derby.
"Strong words were used, reflecting the passion of supporters and their deep disappointment.
"The second-leg tie against Malmo in the Europa League was a nightmare. The manager and players apologised for that after the match. Some supporters felt that was not enough and that more should have been said by the club.
"No-one took any pleasure from the match and everyone shared the embarrassment of our worst ever result in Europe.
"The chairman said the Board and the club are keen to give the players and the manager every opportunity to deliver improved performances and through that, win matches."