The matches had been under the spotlight since the sides were drawn together in February, with Ireland one of Europe's most outspoken critics of Israel's war in Gaza. There have been numerous protests in Ireland asking for the team not to fulfil the fixtures with Israel.
Such was the opposition to the Irish team playing Israel that the Football Association of Ireland chose to hold the game behind closed doors in Backa Topola, a small Serbian town of around 12,000 people, rather than in Dublin.
Reserve goalkeeper Gavin Bazunu, who declined to be in the squad for the first game against Israel, will again be missing when the two sides meet in Serbia on Sunday, and captain Dara O’Shea will also miss out due to the birth of his child.
“Football-wise, what's to come most of all is to control our focus level and keep the focus on that one (Sunday’s game against Israel), don't lose it,” the Icelandic coach told a press conference on Saturday.
“There's been a lot of emotions from the people in Ireland about this, and obviously that affects the players as well. We want to do good, but it's always going to be a challenge when the environment is as noisy as it is.”
Double protest
Thursday’s 2-2 draw with Austria in Dublin was briefly disrupted by two protests, but a superb goal from Troy Parrott against the Austrians and four points from their last two games have dampened the political controversy around the Irish team.
The FAI is continuing to investigate allegations that Irish players Adam Idah and James Abankwah were racially abused in Sunday’s 3-0 win over the Israelis in Hungary.
"It just goes to a process both in our departments and then UEFA to look at," Hallgrimsson said.
"I think it was something that was reported by both teams. I just hope that we can focus on football and that football will be the winner after this."
The 59-year-old said the difficulties the team had faced would strengthen them.
"Surviving this camp, coming out of it together as one, would be a massive win for me, that is coming from my heart," he said.
"I think all the challenges that this team has gone through, all the criticism, yeah, I think just surviving as a group after this game, that will be a big win for me and for this group, (and) for the (football) association."