Thank you for leaving a review of your cruise. A couple thoughts for your next time (and I really do hope you give cruise vacations more of a chance).
1. Carnival and Norwegian (and to some extent Royal Carib) are at the lower end of the popular cruise line spectrum. They cater to singles, couples, and families who have a relatively limited vacation budget. The bottom line cruise cost remains affordable but there are a number of upgrades (e.g., beverage, dining) that are add-ons to that baseline. When budget is really important, at least the basic cruise and essentials are covered. The other side of this coin are that those ships are clean but not terribly fancy and refurbishments take place after longer periods of time.
2. For a nicer ship and experience (e.g., food quality, environment), you have Princess and Holland America (which are part of the Carnival family) and Celebrity (which is owned by Royal Carib). Usually the rooms are nicer (and perhaps larger), the food quality is better, the deck chairs are nicer, the decor is more refined, etc. Nicer means that these lines are more expensive for the above reasons. These tend to cater to couples, 55+, and to a lesser extent families with older children.
3. If you really want to avoid cruises will small children, look at longer itineraries. The 5-7 day cruises are more budget-friendly hence attract families with small children. The 10-14 nighters usually have less of the school aged children. The >14 nighters (except summer & vacation periods) are decidedly mature adult cruises. We just took a 15 day transatlantic trip and I could count on two hands the number of young children and teens that I saw on the ship. Actually, I felt as though I was one of the younger people on the ship :/ and I'm no spring chicken.
4. When researching the ship, go to the line's website and look for a page "our ships" or "our fleet". Example, for Princess the page is: http://www.princess.com/learn/ships/. Check out the details for the ship you are considering to vacation on such as capacity, number of crew, specialty restaurants, etc. The dates of ship launch and last refurbishment are important if you prefer a newer more modern vessel. This also gives you passenger capacity. For us, we stay away from ships with a capacity for over 3,000 passengers. We just don't want to cruise on the mega-ships, preferring the intimacy and limited capacity of moderately-sized ships. Take the time to do some research beyond the itinerary and you maximize the chance of a better overall experience.
That's just a start but hopefully a help. Best wishes for better cruising into the future!