Giovanni Trapattoni's men head for Poznan on Monday night knowing the result of their final Group C clash with Italy is immaterial, at least for them, following defeats by Croatia and Spain.
However, the 31-year-old Sunderland defender is determined to give the fans something tangible to shout about after two immensely disappointing evenings in Poland.
O'Shea said: "It is massively important. We don't want to leave this tournament with three defeats.
"We will be doing everything we can to get something from the game, not just for the fans but from our own point of view as well, the players and the staff.
"We have worked so hard for the last few years in the qualifying campaign.
"Especially for the fans, the numbers they have travelled in and the support have given us, and especially for the tournament and for the group, we will definitely be doing all we can against Italy."
Trapattoni was today [Friday] trying to pick up his players after the most comprehensive defeat of his reign to date - indeed, it was their heaviest reverse in a competitive match for 41 years.
Spain's 4-0 success at the PGE Arena in Gdansk put them in position to ease themselves into the quarter-finals when they meet Croatia, who also have four points after a 3-1 victory over Ireland and a 1-1 draw with the Italians, on Monday.
The Republic were simply unable to stem the tide as they turned in another sub-standard display in the face of irresistible pressure to lose for the second successive match after a 14-game unbeaten run leading up to the finals.
Asked if it had been his most difficult night in football, O'Shea said: "Possibly, yes.
"But you are aware beforehand how well they keep the ball, the number of passes they create in matches and the possession they create in matches.
"It is one of those. You think to yourself, 'Could different systems work? Could different players work?'.
"But you just hold your hands up and say 'stop the mistakes at the start of the game and the start of the second half', and then you have some sort of chance no matter what players or what system you are playing."
Having conceded goals three minutes into either half against Croatia, Ireland were pierced four minutes into either half by the Spaniards, who might have won even more comfortably had it not been for goalkeeper Shay Given.
The 36-year-old, who has not enjoyed the best of tournaments to date by his high standards, produced a string of fine saves, but was also culpable as he and his defensive colleagues wilted in the face of a storm.
Fernando Torres celebrated his recall to the starting line-up by blasting Spain ahead and, after David Silva had taken advantage of panic in the Irish penalty area to make it 2-0, added another with 20 minutes remaining, running away from the green shirts to beat Given with ease.
Substitute Cesc Fabregas made it 4-0 with seven minutes remaining and the final whistle came as something of a relief.
O'Shea said: "We conceded the early goal and, again, the early goal in the second half as well.
"Against a team like Spain, you are just giving yourselves an absolute mountain to climb. Then they can easily pick you off.
"The big thing we have to improve on and what we are disappointed with was the way we conceded the goals. We have been so strong in qualifying.
"Look, as well as that, you hold your hands up and say Spain are an unbelievable team, and if you are giving those chances in the final third you would want to keep Spain to as few chances as possible.
"If you are giving them that encouragement in the final third, it is going to be very difficult for you."
Having seen Spain at close hand, Given is convinced they can retain their title.
He said: "We saw why they are world champions. They cut us apart on a number of occasions and they have got so many great players. The passing and movement is phenomenal.
"If any team can beat Spain, then they will win the trophy. They will be hard to beat.
"We were beaten by the better team. It is obviously difficult to take conceding four goals, especially when you're the goalkeeper."