No, capitalism is not fundamentally "opposed" to government. Government is in fact required for capitalism to function in any kind of efficient manner. If not for the laws governing ownership, ownership would be reduced to the concept of "what you defend, you own", meaning capitalists would have to employ massive armies to protect "their" property, both from rival capitalists and from the people who live or work there.
Capitalism does not require private ownership, e.g. in state capitalism, the state owns the means of production, but the state is not controlled by the working class as it would in the case of Socialism with state ownership. (The difference between capitalism and socialism, if you did not read up on basic political theory, is where the ownership of the means of production lies, with the few (capitalists, whether private or state) as in the case of capitalism or with the people as in the case of socialism (whether by a worker-controlled state or cooperatively by the workers of the particular establishment, to mention only two models))
Also, don't confuse the capitalist economic system with the ideologies advocating keeping such a system, e.g. Liberalism. Capitalism in itself cannot be "opposed" to something, it is an economic system, not an ideology.