Name for that sound you make with pursed lips

I tried searching, but couldn't find anything. What's that sound called, the one you make when you purse your lips and make that kissing kind of sound? I guess people make the sound in different contexts, but for example:

Person 1 does all sorts of complicated things to accomplish a task, Person 2 does it easily. Upon seeing Person 2's method, Person 1 may make this sound.

If there are any Kannadigas, in Kannada it's called lochhguttodu.

Are you thinking of tsking? I realize that the action isn't the same, but I'm not sure there is a separate word for the specific mouth noise you're describing.

interjection, noun
(a sound) used to express disapproval, genuine or mock sympathy, etc.: a click, or sucking sound, made by touching the tongue to the hard palate and rapidly withdrawing it

Perhaps raspberries, as in to blow raspberries:

2 [short for raspberry tart, rhyming slang for fart] : a sound of contempt made by protruding the tongue between the lips and expelling air forcibly to produce a vibration; broadly : an expression of disapproval or contempt

It's known as a bilabial click but that term mightn't be widely understood in the general population, and in linguistics, is a phoneme in certain languages. Note this relevant information from the Wikipedia page:

The labial clicks are sometimes erroneously described as sounding like a kiss. However, they do not have the pursed lips of a kiss. Instead, the lips are compressed, more like a [p] than a [w], and they sound more like a noisy smack of the lips than a kiss. The exception is the rounded bilabial click of Hadza, which is mimetic of a kiss.

And

English does not have a labial click (or any click consonant, for that matter) as a phoneme, but a plain bilabial click does occur in mimesis, as a lip-smacking sound children use to imitate a fish.