It depends a lot on what your relationship with the CEO is like. Do you stop in the corridor for a chat once or twice a week, or is this the first and only time you've spoken directly?
Anyway, I disagree with the answers that say present the facts and make your case. You have already done that. That's what your presentation was. Armed with the results of your investigation, the CEO reached a different conclusion. Since the decision was immediate, I'd guess it's quite likely that the CEO went into that presentation already with an idea of what package she'd prefer to use, thinking, "as long as this investigation doesn't reveal any absolutely fatal problems then I'll go with that". So, there's probably some reason she would prefer to go with "good enough" than with "technically best".
I was tasked with choosing the best software package
Sounds like you were tasked with recommending the best software package. You evidently weren't tasked with choosing which product to use, even if that's what you thought the task was, because that wasn't what you were allowed to do!
The CEO has other priorities than you. For example, she doesn't care whether the app is written in a hodgepodge of Delphi and .NET, or in pure, crystalline, beautiful Haskell. She doesn't care whether she's met the developers or not. She doesn't necessarily want to choose the "best" product technically. Whereas you don't care what your competitor uses.
So if you want to pursue the issue, you should seek to find out what her criteria are for choosing a product. If they are different from the criteria that you used to make your recommendation, then you've learned something about the company's approach to doing business. If they're different from what you were asked to use as your criteria, then you've learned something about what kinds of expertise you're asked to contribute vs. what kind of expertise the CEO prefers to provide for herself. If the CEO's decision still seems wrong even once you know her criteria, then you can ask to present again, addressing the specific deficiencies that you feel she's overlooked.
It's possible that the CEO's criteria are completely misguided. For example, someone might have as a criterion "purchase price must be less than X", overlooking that if the cheap product is hard to use then they'll pay more for it anyway in training and operator errors. Then you'd counter that by quantifying the hidden costs. Or someone might think, "I'm not using anything written in Delphi" and end up overlooking the best product because they rejected it first thing and never assessed it properly. You'd counter that by going through the assessment and showing that Delphi is a red herring (heck, surely part of the point of a cloud service is that they could rewrite it in Delphi any time they like, but this wouldn't affect you). Someone might think, "if it works for our competitor it'll work for us", not knowing that the competitor is preparing to finally dump the rubbish product they've been tied into for years, in favour of a better one.
Arguing that the criteria were wrong is different from arguing which product best meets the criteria, so you need to know the real requirements if you're to do anything other than repeat the opinion that your CEO has already seen you present. The real requirements include more than just use cases.
But the CEO might not want to share the full picture with you -- if that was the plan all along then she'd have delegated the decision, not asked you to present to her for her to decide. If she's left you frustrated that your effort and expertise weren't appreciated then that's a pity, because that probably didn't need to happen, but just because it should have been explicit that you were only assessing one aspect of the decision doesn't mean she's going to change the decision.
Finally accept that the definition of CEO is "person who, if you can't reach agreement in a reasonable amount of time, makes the decision". It's not your job to tell the CEO what to do, it's your job to give the CEO all the relevant information and your expert opinion. And in anything other than a very small company, the CEO can't personally attend to every case of someone disagreeing with them.
that my decision is the correct one
. The world isn't black and white, it is mostly grey. It might even be possible you are wrong here, don't be so sure that your decision is always the correct one. – dirkk May 12 '16 at 9:02