The Republic of Ireland players were jeered by the small number of Israel fans in attendance when they emerged for their pre-game warm-up.
While the FAI confirmed no tickets would be sold to Republic of Ireland supporters, a handful of fans were spotted inside the stadium.
Hallgrimsson confirmed Bazunu would be included in the squad for Thursday’s game against Austria in Dublin, but not for the second match against Israel.
“I think he is very happy that we have won the game,” said Hallgrimsson.
“Nobody was questioning his decision. It was only the timing that was difficult for us to kind of react to it, but none of us were asking him not to take his stand and now he’s flying back with us on the plane.”
When asked if player’s opinions regarding the fixture were taken into account when selecting his team for Sunday’s game, Hallgrimsson said: “Absolutely not.
“This team selection was about who we thought could make the best performance for Ireland.”
During a dramatic day on Saturday, doubts emerged over whether the game would take place after the Republic of Ireland’s pre-match news conference was postponed because of the squad meeting.
When the news conference commenced at 14:30 BST on Saturday – more than five hours later than planned – Courell said a players’ vote on whether to play the game passed by a “significant majority”.
Courell added that the Republic of Ireland would not engage in pre-match formalities such as handshakes.
In 2024, the Ireland women’s basketball team chose not to shake hands with Israel players or stand on court for the anthems before a EuroBasket qualifier in Riga, but the teams did exchange handshakes when they met again last year.
The Republic of Ireland have faced calls to boycott the matches since the Nations League draw in February.
Last November, the FAI approved a motion calling for Uefa to suspend Israel from Uefa competitions.
In May, the team’s friendly against Qatar was interrupted after fans threw tennis balls featuring the Palestinian flag on to the pitch.
In June, the FAI confirmed their home fixture would be played behind closed doors in Backa Topola instead of Dublin’s Aviva Stadium, citing “operational challenges that could impact on the delivery of the game on home soil”.
At an extraordinary general meeting in July, delegates backed an FAI motion to proceed with the games amid concerns that boycotting the fixtures would cause “significant and lasting harm” for the association.
Calls for the Republic of Ireland to boycott the games have intensified in recent weeks. Earlier this week, more than 160 Irish athletes signed an open letter by Irish Sport for Palestine group urging the team not to play.
Courell also said last week Uefa had rejected a request for the Republic of Ireland and Israel to be kept apart in future competition draws.
Tensions between the teams were raised this week when the Israel Football Association accused Hallgrimsson of “ignorance, hypocrisy and stupidity” after the coach said, “we’re not playing with genocide, we’re playing against genocide”.
Speaking on Saturday, Hallgrimsson said it was “a wrong word for me to use”, while Israel FA head of communications Shlomi Barzel said he would not apologise for his association’s response but said he would “take back the word stupidity”.
The armed Palestinian group Hamas attacked Israel on 7 October 2023, killing about 1,200 people and taking 251 hostages.
In response, Israel launched a massive military offensive in Gaza, during which more than 73,000 people have been killed, according to the territory’s Hamas-run health ministry, whose figures are considered reliable by the United Nations.
Israel has repeatedly denied that it has committed genocide, as well as war crimes and crimes against humanity. It says its military operations in Gaza have been conducted in self-defence and in accordance with international law.