Words like egotistic or egotistical ("Believing oneself to be better and more important than others") may apply, as may egocentric ("regarding oneself and one's own opinions or interests as most important or valid") or narcissistic (as used in phrase narcissistic personality disorder). More generally, terms like realistic or unrealistic may apply, depending on whether subject's opinion is correct or mistaken. In some cases, one might call the person a Pollyanna ("person who is persistently cheerful and optimistic, even when given cause not to be so") or Panglossian ("having the view that this is the best of all possible worlds").
Regarding positive or negative connotations of these and other words, among the set of near-synonyms aloof, arrogant, blustery, boastful, bombastic, cocky, conceited, egotistical, flaunting, grandiose, haughty, insolent, narcissistic, ostentatious, pompous, pretentious, self-important, supercilious, uppity, vainglorious, vain, big-headed, high-and-mighty, show-offy, snobbish, snotty, snooty, stuck up, nose in the clouds, holier-than-thou, in my estimation all carry some negative baggage, and those with the least-negative senses include arrogant, egotistical, flaunting, and supercilious; and of those four, only egotistical is adequately close to the meaning requested in question. Note that self-righteous is a rather more negative label than egotistical. Realistic, if you can apply that label, is positive or neutral, and unrealistic is negative or neutral.
I have said terms arrogant, egotistical, flaunting, and supercilious are less negative than others, partly as a consequence of how similar terms are used in Aristotle's Nicomachean Ethics, as for example the lengthy discussion of pride in Book IV part 3. However, the slightly-technical usage there is uncommon, so only a weak basis for comparison.
Best Answer
I don't think you're going to find a single word, because pride has two aspects to it:
I think the easiest thing would be to use a word that means pleasure/satisfaction and then just say why this feeling has been elicited.
You could use the word from your own post: pleased:
Or perhaps the word glad:
Both of these avoid the gushing nature of proud.
Depending on context, you could use an intensifier such as really glad.