For example, I have to proof statement: if random variables $X$ and $Y$ are merely marginally normally distributed and uncorellated it is not enough to deduce the normality of the vector $(X,Y)$
I found a counterexample, that will show the truth of statement. Is it enough for proof?
I'm not entirely clear on what you're asking, but I'll try to answer anyway.
A "counterexample" is an example that demonstrates the falsehood of a statement. For example, if I say "All swans are white", then a black swan would be a counterexample.
A counterexample is always enough to prove a statement false; if I can supply a black swan, then "all swans are white" is certainly false. But an example is never enough to prove a statement true - a single white swan is nowhere near enough to prove that "all swans are white" is true.
So if by "I found a counterexample that will show the truth of the statement" you mean you found a pair of random variables that are marginally normally distributed and uncorrelated but the vector $(X,Y)$ is not normal, then yes, that's sufficient proof. If you mean that you found a pair of random variables that are marginally normally distributed and uncorrelated and the vector is normal, that's not enough to prove the statement.