The Leith outfit lost their first match since the 44-year-old Irishman resigned when they went down 1-0 to Motherwell at Fir Park.
But Hibs chief Petrie declined to comment on speculation Butcher is now the man he wants to take the club forward.
He told BBC Radio Scotland: "I think Pat Fenlon did a good job but he's made his decision and we are looking forward now. I'm not going into any names. It's important that we take our time and get the right guy."
The Northern Irishman was visibly saddened to see Fenlon go but thought he had managed to persuade the former Bohemians boss to stay on in the capital following Wednesday's humiliating loss to city rivals Hearts in the League Cup quarter-finals.
He said: "I tried to talk Pat out of resigning. For a good length of time and I thought I had him too. But deep down I could see the relief in him once he had made his decision.
"Can I understand his reasons? No, and I told him I thought he was going for the wrong reasons.
"But then when you watch the interview after he announced he was leaving, you can see the weight coming off him.
"It's okay me saying to him that I enjoy working with him and that it will be alright. It's okay me telling him he has got the respect of the players and that he has turned this place around, but I am only talking football to him. But he has got his personal reasons and you could see the relief in him now."
The derby defeat by the financially-stricken Jambos - the second time it has happened this season - was too much for some Hibs fans who protested after the midweek upset.
It comes after the record 9-0 aggregate Europa League defeat to Malmo and of course, last year's 5-1 disastrous Scottish Cup final loss at the hands of the Tynecastle men.
But Nicholl says the fans did not see the full impact of Fenlon's efforts.
"I've only been at the club a short while but the boys who have been there longer tell me what a difference Pat made and what it was like before," he said.
"But it's everything else, the fans are only interested in winning games and cups. But what Pat did behind the scenes matters to football people and he can go away knowing that."
Butcher has emerged as the bookies' favoured candidate but Nicholl says he hopes to remain with the club, no matter who takes over.
"I haven't taken any phone calls from any of the candidates," he joked when asked if he had talked to his former Kilmarnock boss Kenny Shiels.
"I want to stay at the club, though. I just stay below the radar. Whatever happens. happens. If whoever comes in wants me to stay then brilliant. If they don't, then that's it."
While Hibs now await the identity of the man who will take them forward, there was relief for Motherwell as they bounced back from their own League Cup exit at the hands of Aberdeen on Wednesday.
Hibs striker Paul Heffernan wasted three great early chances to give his side the lead and was punished as McManus headed home from Lionel Ainsworth's corner.
The home side then lost Shaun Hutchinson to a straight red card three minutes from the end after he tugged down Heffernan as the striker ran through on goal, but they held firm under pressure to collect the win.
Boss Stuart McCall took that 2-0 defeat to the Dons to heart but was pleased to see his side return to winnings ways.
"I felt so low after the Aberdeen game and it was a combination of things," he said. "Aberdeen have now knocked us out of the cup three times in a row and every team knew it's not often you can get into a semi-final that doesn't involve the Old Firm. The teams now in the semi-final won't have a better chance of winning a trophy.
"So to win is a massive relief because it has been a tough week. We were hanging on at the end, there's no doubt about that, but it was a gutsy display. It was a deserved three points if you look at the chances over the piece and it is a massive relief."
- Sports & Recreation
- Pat Fenlon
- Jimmy Nicholl