What makes you think Italy was a great power then? Italy was not unified until 1866. Prior to WWI, the only incident I can think of in which Italy was involved in international affairs was when it joined the eight nation alliance which suppressed the Boxer Rebellion.

Italy was a great power because it was a large unified state with a homogenized population and a powerful economy. That it was for certain measures of large, unified, homogenized, and economically powerful at least. It was never a state on the UK's or Russia's level. In most ways they were the "least" of the great powers. And a lot of politicians at the time didn't place them in the ranks of the great powers. The traditional list of European great powers post German unification was Austria, France, Germany, Russia, UK... and maybe Italy.

Here are some stats. Dates are as noted. Statistics are all from Paul Kennedy's, Rise and Fall of the Great Powers

Population (1890): Italy was the smallest "great" but not by bunches. With 30 million they were in the rough neighborhood of France (38.3 million) and the UK (37.4 million).

Industry (1880): By virtually any measure Italy was industrially behind. They were 5th in per capita industrial production, behind the UK, US, France, and Germany. But in absolute terms their smaller population left them as the least for iron production, energy use, and total industrial output. They produced 2.5% of the worlds finished goods in 1880. This compares reasonably against Austria's 4.4%. But the other European great power competitors were between 7% and 9% and UK and US were outstripping everyone at 22.9% and 14.7% respectively.

Military (1890): This is where the Italians clearly made their push. They wanted to be taken seriously. And so they fielded a serious army and navy. Their total personnel was 6th in Europe (funny how on so many rankings that's where they end up, 6th). But it was only 60,000 behind their closest rival Austria. And it was twice that of Japan and the US combined. And their warship tonnage was 242,000. This gave them the worlds 3rd largest navy after the UK and France.

So all of this should highlight Italy's relative position. They were absolutely in the top 10 most powerful countries in the world in the 19th century. They probably weren't in the top five. So it depends on where you draw the line of what a great power is. In a European war they were, as I said, viewed as number 6.

Even today a century and a quarter later they hold a similar position. And they have held it pretty consistently. For most of the 19th and 20th century they were a top 10 power. They have slipped a bit. Today they have the world's 23rd largest population, the 9th largest economy (they are number 5 in the G-7 but have been passed by non-members Brazil, China, and Russia), and The GFP Index ranks them as the 12th most powerful military in the world.

Maybe the reason we don't think of them as a great power today, is because the super powers made great powers passé. Or maybe it is because they are where they were 130 years ago, on the cusp of where we expect a global player to be. They aren't a major regional player like Brazil or India. They are a significant voice in the EU, but less of one than Germany or France.