There's nothing wrong with mentioning specific songs or tech in this way.
And while it's not lazy writing to use songs as a tool for conveying a character's mood it is to rely on them solely. Expecting the reader to take them listening to a particular song as meaning they are sad just isn't going to work (unless you've already somehow established that as being their go-to "I'm sad" listen!). Humans can have both semantic and episodic musical memory and the contents of both will vary from person to person.
Semantically the Gary Jules cover of Mad World for me is things like who played the piano (Michael Andrews), what film it was recorded for (Donnie Darko), when it was released (2003) and so on. It's facts not emotion. For the emotional aspects you have to go to the episodic memory - and for me those are happy memories (I enjoyed the movie, I saw it at a happy period in my life etc.)
So if you're looking for a reader (in this case me) to realize your character is sad and to empathize with them you're out of luck.
And if I'm honest there really isn't much else in the snippet to point me that way either:
The Autumn leaves were falling
Tells me the time of year - it doesn't really convey much about mood though. You can use weather to help establish mood but rarely in isolation. Autumn leaves are not in themselves inherently sad - they are a popular tourist attraction in parts of the United States!
as I was sitting alone
Tells me the POV character is alone. Unless there's preceding information that this likely to be something that they either do when depressed or is something that would cause them to be depressed it indicates nothing more or less than that they are alone in this scene.
Your comment on another answer:
Actually, I have already made it clear to the reader that she is under depression and in just next paragraph I had added emo-lines from the song.
Confirms that we are firmly in "lazy writing" territory here. At a wild guess I'm going to say those quoted lines include either:
Their tears are filling up their glasses
The dreams in which I'm dying are the best I've ever had
or both. You aren't using your words to show me how the character feels - you're using someone else's. If the intent is to show that the character is a person who takes "emo" lines to heart as if they are y'know..really deep, then that's a different thing and I don't think that's what you are aiming for.
You've got scenic elements in the snippet that could be used to provide a lens on the character's mood and state of mind - you just need to take those opportunities:
I was sitting by myself, watching the autumn leaves fall. The piano notes of Gary Jules' Mad World playing on my iPod giving each slowly tumbling leaf a melancholy sound track which suited my mood. I was alone.
There's the same key elements of your original but they are tied together - and to the character's state of mind to set the scene. You can tell that the character is feeling melancholy by how they perceive their surroundings.
Also note that the attributes of the song that are necessary for the effect are described. That way it may be beneficial for the reader to have heard the song but it's not required. In the original wording if the reader is unfamiliar with the song, or potentially even worse if they are merely familiar with the original version of the song,(which is an upbeat synth-pop track!) you risk conveying no emotional cues or even opposite emotional cues to what you intend.