If your goal is to create a company that is going to be around in its original form and that will 'change the world' then by all means, stick around.
But if you create 'web-apps' for an emerging field where you'll be faced with 10's if not 100's of competitors a successful acquisition is not bad at all. In such markets shake-outs are the norm, and that period is marked by acquisitions and obituaries.
Most successful start-ups find that at some point in time they're going to be acquired.
Your comment reminds me of the criticism levelled at mint.com when they 'sold out', as though what they achieved and did was all negated by selling to their 800# gorilla competitor.
Personally I think they - and Peter Cooper, albeit at a lesser scale - did great.
Whether you should stick around or not depends on a lot of factors, your ambition, your ability to manage a larger company (and your desire to do so), your risk profile and so on.
No one size fits all, there is room enough for all strategies and tactics, what works for you may not work for everyone. Peter managed to do what very few people here will ever manage to do, in spite of all the potential, he did it under his own power, recouped his investors money and paid them a premium, had a pretty much text-book acquisition for a company this size. Nothing to complain about.
Could you do better ? Maybe. But you could also do a lot worse.
The joke goes that no deal is ever right, if you manage to sell you should have waited, if you crash you've waited too long.
So a certain feeling of 'I could have done better' post sale is pretty much the norm, and maybe you really could have done (a lot) better, but for all the same money you'd have crashed horribly or you could have found yourself the proud owner of a stagnant business in a field with lots of better funded and better executing competitors. There might be a way to turn that around but it's not a given.