Genocide is usually defined as, "the deliberate and systematic destruction, in whole or in part, of an ethnic, racial, caste, religious, or national group".

The potato famine was not deliberate. Nor was it systematic. It did reduce the population of Ireland by circa 2m people (half by famine, half by emigration) or by about 25%.

It was tragic, of course. And the British government response was ineffective. (The British did try various means to relieve the famine, and spent 8.3 million pounds on famine relief, but their efforts were not well planned, coordinated, or enough.)

Source: http://irishpotatofamine.net/british-governments-role/

The ineffectiveness of the famine relief efforts may have been partly due not only to incompetence, but to indifference, or even to opposition by some (either in Britain or among Irish landlords). On the other hand, even before the famine, Britain had a hard time achieving good government in Ireland.

In 1844, one year before the famine started, Benjamin Disraeli asked, how do we govern a country which had, "a starving population, an absentee aristocracy, and an alien Church, and in addition the weakest executive in the world."

Between 1800 and 1845, the British government had run 114 commissions and 61 special committees inquiring into the state of Ireland and making recommendations. Most of them prophesied disaster, as the population was increasing rapidly. Poverty was widespread. Hunger was common. One quarter of the population was unemployed.

That there was a problem in Ireland was known. That the potato blight would accelerate that problem into calamity, of course was not.

What was it about the situation in Ireland which prevented the government from making improvements, or from effectively relieving the famine?

That's a complicated question, but it probably has its roots in the system of land ownership, and how the land owners managed to wield enough political power to snarl and confuse efforts to reform or relieve Ireland, without exerting enough leadership or control to manage such efforts themselves (even if it might have been in their long term interests - though another hypothesis would be that they did not see it as in their long term interests).

Particularly tragic, was that an effective counter measure to an Irish famine had been deployed before, but was not used this time. When Ireland had experienced a famine in 1782–1783, ports were closed to keep Irish-grown food in Ireland to feed the Irish. Local food prices promptly dropped. Merchants lobbied against the export ban, but government in the 1780s overrode their protests.

No such export ban happened in the 1840s.

Source: http://en.wikipedia.org/wiki/Great_Famine_(Ireland)

In short, though the Potato Famine was a terrible and tragic disaster for the Irish people, it was not a "Deliberate and systematic destruction", and so was not a "genocide".

No. Genocide is a form of murder, which requires an intent to kill. There was no intent to kill in the Irish Potato Famine. Although it is often blamed on the British, the famine was caused by a potato blight, which had also affected Scotland and the rest of continental Europe. The famine effected Ireland greatly because of the importance of the potato in the diet there.

What "did the damage" was the laissez faire economic policy at the time. This meant that the govt. was unwilling to intervene in the famine unless it upset the balance of the economy, and they expected that the market would provide the food needed to feed the starving. Instead, the govt. started schemes such as building roads in order to give people wages so they could feed themselves- even though these jobs required hard manual labour which starved people could not do effectively.

I asked this question a year ago and got some pretty good answers, so you might want to check there too.