Araibi was held in a Thai prison for more than two months at the Gulf state's request before arriving in his adoptive home Australia on Tuesday to cheers from hundreds of supporters.
The 25-year-old fled Bahrain in 2014 after being accused of crimes committed during the 2011 Arab Spring protests, which he denies, and received refugee status in Australia. He had travelled to Thailand for his honeymoon.
"We have been working for this solution through official channels obviously. We have been working as well behind the scenes," Infantino told a news conference in Istanbul when asked about criticism over the lack of FIFA public statements on the case.
"I prefer not to make any press conferences or any big statements. I prefer to have results. This is how we are working at FIFA," he said at the end of a FIFA summit in Istanbul.
"I think we can celebrate the fact that everything ended in a very positive way, and we are just happy about that," Infantino said.
"It is not the merit or no merit of anyone in particular; it's all those who have contributed," he said.
Araibi had been convicted of vandalising a police station in Bahrain and was sentenced to 10 years in prison in absentia.
He has denied any wrongdoing, saying that he was playing in a televised match at the time the offence was committed, and was granted asylum in Australia in 2017. Bahrain, however, sought his extradition from Thailand.
He was freed after nearly three months of diplomacy, legal manoeuvring by the governments of Australia, Thailand and Bahrain, and a public campaign by footballers and human rights activists.
(Reporting by Daren Butler; Editing by Hugh Lawson)
