Anier came off the bench to score the only goal of the Scottish Premiership clash at Easter Road after the Hibs defence was caught flat-footed for the second time in quick succession.
Hibs now face a pressure derby at administration-hit Hearts next Sunday but Fenlon felt they had made a largely solid start and pointed out that they had lost 3-0 at Dundee United on the opening day last season before recovering quickly.
Some supporters booed the team off, although others applauded, and the Irishman admitted he might have been the focus for the jeers.
But he wants the focus to be on his team improving rather than his own position.
"I don't know whether they booed the team off or booed me off," he said. "I understand why the supporters are frustrated. When you lose matches you are never happy.
"You have to be big enough and strong enough to take it on the chin.
"If they are booing me, it's not relevant from my point of view. That's frustration. If I were up there, I'd probably be doing the same.
"I've said from the start, if I can take this club forward, brilliant, it's a fantastic football club. If I can't, then someone else comes in.
"I'm disappointed we have a lost the game but we started much better than we did last year at Tannadice."
Anier was sent clear by Stephen McManus's headed clearance in the 83rd minute, six minutes after Ben Williams had saved from John Sutton after the hosts were caught out by Iain Vigurs' ball over the top.
Fenlon, who revealed Alex Harris had been taken to hospital with a swollen ankle, added: "It's a sore one to take, I didn't think we deserved to lose.
"There was some positive stuff but we lost the game to a poor goal and I'm disappointed that the good stuff will be forgotten.
"Defensively we were solid. I thought we had dealt with Motherwell's shape and (James) McFadden coming into the hole to pick things up, and then we got done by a long ball over the top when we were attacking.
"They were the only two real chances they had, the first came from us losing the ball at our throw-in and then a punt over the top. We were ball-watching and Ben made a good save."