The Boys in Green went into their final 2024 UEFA Nations League fixture at Wembley Stadium on a high having defeated Finland earlier in the week.
That victory ensured that Republic of Ireland would keep their place in Tier B of the competition, and there were positives that would have been taken from how they stifled England during the first half on away turf.
However, triggered by the dismissal of Liam Scales who conceded a penalty which England scored from, Hallgrimsson's side capitulated after the break.
Harry Kane, Anthony Gordon, Conor Gallagher, Jarrod Bowen and Taylor Harwood-Bellis all got on the scoresheet during 26 second-half minutes.
What did Hallgrimsson have to say?
Speaking to RTE after the game, Hallgrimsson admitted that a "crazy moment" had swung the game in England's favour.
Nevertheless, the 57-year-old felt that there was reason to question whether his players gave their all during a one-sided second half in London.
He said: "First half was like we wanted it but it's easy to say we had a good first half but when you lose 5-0 there's nothing you can say."
"It was six, eight minutes of madness, ending up with conceding a penalty. Losing the ball is one thing, not reacting is another and conceding a penalty, losing a player, it was a lot of shock. 1-0 and then in your face you get a second and I just felt we lost our heads at that moment. After that, there was no way back.
"We kind of just gave up. Easy to stand outside and criticise the players but it was a crazy moment that killed everything, not only the gameplan but the momentum and fight seemed to be taken away from them.
"There is hardly anything I can say now. You try to pick the positives and the positive was the first half."
What next for Republic of Ireland?
While Hallgrimsson cannot be satisfied with his team's efforts in a group that also featured Greece and Finland, remaining in the second tier of the Nations League is a respectable achievement for a team sitting in 63rd on the FIFA World Rankings.
That said, Republic of Ireland failed to score a single goal in their four fixtures with England and Greece, leaving Hallgrimsson with food for thought.
Republic of Ireland will play two friendly fixtures in March having missed out on a playoff spot.