Newco Rangers had their Scottish Premier League application rejected last week and many clubs may suffer financially whilst the Ibrox club are not in the top flight.
Fenlon has acknowledged the need for caution but also revealed he hopes to add more players to his squad before the start of the new campaign.
“I think it (the Rangers situation) has affected everyone,” he said.
“We have just got to be careful and astute with what we try and do. We are not going to be in a position to match what has gone out of the club but we are in a position to bring some players in to strengthen it.
“We don’t have a big squad and we need to add a few more to it and if we can do that we will be delighted.”
A host of players departed Easter Road at the end of last season after their contracts expired and former Bohemians boss Fenlon is now looking to shape the squad to his own liking after taking the job at Hibs in December.
“We let 14 or 15 players go and we are not going to be in a position to sign that many players but we have brought in four and we are hoping we can bring in a few more to strengthen the squad,” he said.
“What we want to do is build our own squad. We have done that by starting with players leaving and players coming in.
“Having the time to work with the players in pre-season obviously means you can put your own slant on things as well and we are happy with how things have gone so far.”
An 11th-placed finish last season was a disappointment for the club and reaching the Scottish Cup Final was tainted when they were beaten 5-1 by Edinburgh rivals Hearts.
Fenlon has refused to use the high-profile thrashing as motivation for the upcoming season.
“I don’t think we need to use that (the cup final defeat),” he said. “Last year was disappointing for the club and the year before that was also disappointing for the club so we shouldn’t need any impetus to do better.
“You look around the place and this football club should be doing better than it is and I will do my best to do that and I hope to God we can get this club back to where it should be.”