The England international terminated his contract at Al Ettifaq just six months after a lucrative transfer from Liverpool in order to sign for Ajax.
Henderson was widely criticised for his move to Saudi Arabia, where same-sex relationships are illegal, after becoming an important ally for the LQBTQ+ community during his time in the Premier League.
Speaking at a press conference on Friday, the 33-year-old said: "If any people from that community feel let down or hurt I apologise.
"If anyone was offended or feel as though I upset them, that's on me, that was my decision and I apologise for that. It was never my intention.
"I just want to look forward now and concentrate on being the best player I can for Ajax. My beliefs have never changed and never will. Again I can only apologise if people feel let down."
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talkSPORT understands Henderson left Saudi Arabia without receiving any of the £4million he was owed from his £8m annual salary, having deferred his wages for tax reasons.
Moreover, the midfielder could be forced to pay Al Ettifaq from his own pocket if performance-related clauses are met in the Eredivisie.
Nevertheless, Henderson refused to give a negative reflection on his nightmare experience in the Saudi Pro League.
"In life, if you want to call them regrets or mistakes, you can call them that. But they are only mistakes if you don't learn from them.
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"I learned a lot of things out in Saudi. There were a lot of different experiences. I haven't got a bad word to say about anyone over there, the league, the club.
"The people tried to make us feel as comfortable as possible - and my family. I've got friends over there who I will talk to forever.
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"There's still positives to come out of it. In the end, it didn't turn out the way we wanted it to, but we ended it on great terms.
"We'll shake hands and move forward."