Xjyuk

Is there a word for the selfish kind of (possibly humourous) delight felt at someone else's failure?

e.g.

No matter how I tried, I couldn't complete the seemingly simple task. So feeling like an idiot I gave up and asked the expert. But to my ______, he couldn't do it either!

There is an English word for this - epicaricacy. However, it is not a widely known or used word. I would say that more English speakers would be familiar with the German borrow-word schadenfreude, but even that may be limited to well-read persons.

A person who derives enjoyment from the suffering of others is a sadist, and while this carries a very strong and serious meaning, it is possible to use it in a lighthearted, softer way, for example:

He derived a certain sadistic pleasure from the misfortune of others.

Although sadism involves the inflicting of misfortune on others, the term "a certain sadistic pleasure" is used in a more vicarious way such as this quote from the NY Times:

...some of the people are so unpleasant that there's a certain sadistic pleasure in witnessing the awful things that happen to them.

However, I think the best word to fit into your sentence is "amusement":

No matter how I tried, I couldn't complete the seemingly simple task. So feeling like an idiot I gave up and asked the expert. But to my amusement, he couldn't do it either!

You do not really need the word to carry the meaning of epicaricacy because your sentence makes it quite clear what you are deriving amusement from. Your statement is more a definition of this kind of pleasure.

I'm thinking about the word gloat:

To feel or express great pleasure or satisfaction because of your own success or good luck, or someone else's failure or bad luck.

• A disaster for the media, but worth a gloat from everyone else




• I know I shouldn't gloat, but it really serves him right.




• His enemies were quick to gloat at his humiliation.

But to my perverse satisfaction he couldn't do it either!

"marked by a disposition to oppose and contradict"

Source: Vocabulary.com

Example:

"He gets perverse satisfaction from embarrassing people."

Source: Longman Dictionary

Relish, gratification

As an antonym of the word sought, chagrin (Merriam Webster), could be used to emphasize the vexatious nature of a feeling, as in "...to my chagrin, he was able to do it easily".

Looking up antonyms of chagrin (power thesaurus) turned up relish:

relish [noun] ...
3.2 enjoyment of or delight in something that satisfies one's tastes, inclinations, or desires (MW)

So as a single word answer you could say

But to my relish, he couldn't do it either!

Gratification (C.E.D.) also combines meanings of pleasure and personal satisfaction. With slight rewording for emphasis you could also say:

Much to my gratification, he couldn't do it either.