Hodgson admitted back-to-back defeats to the Scarlets earlier in the group stage was the real reason for the Exiles' elimination and feels there needs to be a change in mentality if the team are ever going to start challenging for honours.
"We haven't lost to the Heineken Cup champions in either of our group games," he said. "But it's in the games where we perceive teams as no threat where we need to get better.
"The best teams do lose games. I accept that, that's fine. It just can't happen too much because if it does, you find yourselves out of the four in the Premiership and out of competitions.
"If you can bottle the way we prepared for this game, and against the likes of Saracens, Leinster away, Wasps and Leicester, we'd be fine. On our day, we can beat anybody, we just have to do that for every game."
Hodgson insists winning the Premiership remains the ultimate goal for Irish and without Europe to distract them, this just might be the year to do it.
They came so close last season, losing 10-9 to Leicester in the final as another golden opportunity went begging, but they find themselves well placed this campaign too, just four points off leaders Leicester with a game in hand.
Hodgson added: "Injury-wise, the squad's in good shape so we should just go for it. We've talked about that being the one we wanted for a couple of years now. We came very close last year and we want to go one better."
Northampton are the Premiership's sole survivors in the tournament, making it the worst display by English clubs in the event's 15-year history. And faced with the prospect of an away quarter-final at two-time champions Munster, Jim Mallinder's team have a mountain to climb.
Leicester went out in controversial fashion against Ospreys, with the Welsh side guilty of having 16 players on the pitch at one stage in the second half when Lee Byrne returned to the action after a blood injury without replacing a team-mate.
The Tigers lodged a complaint to European Rugby Cup but the 17-12 score is likely to stand.
It is expected Ospreys will escape with a fine for their mistake.
