"I just think we didn't take our big moments, even though we had momentum, and they did," said Terland, who was introduced in the second half to chase a second goal for Norway. "It's those moments that win you the game, so unfortunately, it went like that today."
Norway looked like they had the edge as their Women's European Championship quarter-final approached 90 minutes with the score tied at 1-1, but Girelli's late header off a deep cross from Sofia Cantore dashed their hopes.
The 2013 finalists had gone behind when Girelli got her first goal early in the second half and their misery was compounded by captain Ada Hegerberg missing a penalty.
But when Hegerberg equalised in the 66th minute, the pendulum swung in favour of the Scandinavians, only for Italy to deal a late knockout blow.
"It was a first half in which Italy were best, but we improved ourselves in the second," said Norway defender Maren Mjelde. "We had good control, and then suddenly they seemed to get a goal out of nothing."
The Italians had targeted Norway's right flank all night with Cantore's precise delivery catching the Norwegian defence off guard.
"We knew that they were good at crosses and in the box, they got a lot of players in the box, and it's tough to stand here now," Mjelde said. "I thought we'd get to 90 minutes and then maybe restart."
Italy will face the winner of Thursday's quarter-final clash between Sweden and England in Zurich.