Ok, so technically, no matter cash game or tournament, cards speak. When in doubt just turn the over. In the case of an all-in, again technically you should be turning the cards over. In a tournament this is pretty much always enforced.
Cash games however people are often given pretty big allowances on this and it isn't expected to show the cards if you declare that you've lost. HOWEVER as mentioned above, technically you should turn them over, and be aware the other player in the all-in has the right to see them if they ask. Some people consider that bad etiquette.
I wasn't 100% clear on the situation, but another way I read it is that you said "You got it" on the turn. Just because you said you got it before the river doesn't make that a binding true statement on the river. Your hand wouldn't be binded to a fold, as a hand cannot be folded when it's all-in. It can only be mucked on the river. Best shown hand wins at showdown, always in an all-in situation.
So in your situation, if you haven't turned your cards over, and have declared that you have lost, due to it being a cash game, and even though cards should technically be shown, it wouldn't be enforced and your hand would be mucked. It sounds like you made a mistake here and unfortunately have to bare that cost.
One caveat to the above, if you realise that you actually had the winner, while your cards are still with you, even after verbally declaring, as long as you turn them up you'll win. Cards speak loud. When in doubt turn them up and let the dealer sort the winner.