The closing stages at Easter Road saw Ryan McGivern cancel out Sammy Clingan's opener, before the visitors immediately regained the lead through Jude Winchester - only to have this cancelled out through Leigh Griffiths just seconds later.
And Fenlon admitted his side switched off following McGivern's equaliser, relying on Griffiths' late flick to save a point at Easter Road.
"The annoying thing is that we scored the goal and got carried away," said Fenlon. "The crowd were right into it, they wanted to push us on and it is difficult.
"The players have to realise you have to steady yourself after scoring a goal, to keep your shape because you see teams conceding after they've scored quite a lot.
"From their point of view it is a good goal but from our point of view we could have dealt with it better.
"To concede a goal that late is a hammer blow but credit to the players, they kept going and got an equaliser."