The spirited visitors surged into an eighth-minute lead through a great goal from John Baird - and only an equally impressive Leigh Griffiths free-kick earned the hosts a point.
The fourth-placed Hibs were expected to overcome Barry Smith's rock-bottom Dark Blues with ease, and Fenlon admitted it was a disappointing showing after solid performances against Celtic and Hearts.
He said afterwards: "We just looked lethargic. It took us too long, we never started the game. Dundee started well and I suppose we only got going in the second half.
"We had started really well in the last two games and we just didn't have the focus today.
"We didn't start on the front foot, the first pass was sloppy and it went from there. We were too loose and didn't have the right tempo. We didn't play well today and we know that."