lie algebra cohomology

Question

Suppose that I have a semi-simple lie algebra $\mathfrak{g}$ and I have a linear map from a vector space $V$ to $\mathfrak{g}$. This map is surjective. Can I show that the corresponding map from $V$ to $G$, the corresponding lie group, is also surjective? The Lie algebra $\mathfrak{g}$ is semisimple and I know it has trivial cohomology, then I have the intuition that I can extend the properties for the lie algebra to the lie group, since it has no obstruction. But this is only a intuition and I dont know how to do it precise