Skipper Caelan Doris said that the title scenarios were not a huge focus during the week but thought they had an impact as the game wore on.
Ireland went behind through Monty Ioane’s try in the 12th minute before leading 12-10 at the break thanks to scores from Hugo Keenan and Sheehan.
Sheehan scored two second-half tries to complete his hat-trick but Ireland could not press home their advantage and finished the game requiring a defensive stand to see out the win.
“It wasn’t something that was overly pushed or anything during the week because of the respect we have for Italy and their attack, what their capable of,” said Doris of the need to rack up points.
“It was very much ‘result first’ but there was probably a little bit of feeling when momentum was coming with us, given how the first 20-30 went, that we wanted to convert when we got the chance.
“Maybe there was a little bit of forcing things out there. There were quite a number of last passes that didn’t go to hand. Why? Maybe forcing things, I’m not sure.”
Ireland won their first three games of the championship, securing the Triple Crown against Wales in Cardiff last month.
Their hopes of a Grand Slam, however, were ended by a heavy defeat by France in round four.
“I think there’s been a lot of good stuff,” added Doris of the campaign as a whole.
“Our first three games, winning the Triple Crown within that, showed quite a lot of positive things in there.
“There’s lots of things we can learn and grow from over the last couple of weeks and I hope that it will be a springboard for us as a group to go and continue to evolve and a bit of a realisation that there’s still a lot of work to be done and a lot in us.”
