The Whites boss says supporters have every right to be unhappy.
Against Rotherham United on Saturday with the game level at 1-1 and the Millers down to 10 men, Giuseppe Bellusci's mistake gave away possession in the final minute and Whites goalkeeper Marco Silvestri was sent off for bringing Lee Frecklington.
With all three substitutions already made, Bellusci had to go in goal to face the penalty, which was converted by Greg Halford to consign Leeds to defeat in disastrous fashion.
That loss followed a 4-1 home thrashing by Huddersfield Town a fortnight ago before the international break as the Elland Road side's brief revival was cut short in brutal fashion.
Evans admitted to BBC Radio Leeds that Whites supporters have every right to be unhappy with how things are going for the club at the moment after consecutive defeats to local rivals.
He said, as quoted by the Daily Star: "They are entitled not to be happy. We've lost two derby fixtures.
"We lost badly against Huddersfield, we didn't lose badly [to Rotherham], we lost through someone not doing a basic bit of defending."
What makes the double defeat even more painful for Leeds fans is that they have followed a period during which the club were looking as though they may have turned a corner.
The Whites won three successive games in early March, beating Bolton Wanderers, Cardiff City, and Blackburn Rovers after a run of just one victory from the previous 11 Championship matches.
The latest defeats, however, leave Evans' side in 14th place as they look to turn things around against Queens Park Rangers at Elland Road on Tuesday night.