The Hoops rejected a £25m bid from Nottingham Forest for the Belgium international in the winter transfer window and Engels was keen for a move to English football.
Speaking at a media conference ahead of Saturday's Scottish League Cup second-round tie against Dundee United, O'Neill said: "West Ham wanted him to be available for the opening day of the season. Naturally disappointed, really, that he's leaving the football club, he's done very well for us.
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"And it's hard to dissuade him of that. If it hadn't come up, I think he'd have been happy. Even though the offer came in very late from Nottingham Forest in January, he never moaned about it at all.
"So it's an opportunity for him and it's really hard for him to turn it down."
Engels moves ahead of Celtic's Champions League play-off first leg against LASK next Wednesday but O'Neill understood why Engels was keen to complete the transfer, especially after Alistair Johnston suffered a leg muscle injury amid interest from Everton.
"Ideally, I'd love him to have stayed and maybe completed after the two games," said the 74-year-old, who is fully back to work after a medical procedure last week.
"It probably wasn't going to happen. You've got a concern, I suppose, with the fact that Alistair played for us when there was an offer on the table, hurt himself, maybe things like that there may disappear.
"I suppose Arne was probably worried the same sort of thing might happen. From a playing viewpoint, I probably can understand that."
Canada right-back Johnston went off at half-time in Celtic's 5-1 win at Kilmarnock on Sunday.
"He'll be out for a few weeks," O'Neill said. "By the time he's fit, he'll be past the transfer deadline. He's been very stoic about it, really.
"It's a shame for him but it's not long-term. It's something that he'll get over and he'll be back."
Celtic signed Egypt winger Haissem Hassan and Germany Under-21 midfielder Mika Baur this week and O'Neill expects further arrivals.
One could be Chelsea left-back Landon Emenalo as a loan back-up to Kieran Tierney after the 18-year-old was given a tour of Celtic's Lennoxtown training centre this week.
"I think he's a really fine young player," O'Neill said. "Obviously we need that position covered. Kieran did exceptionally well last season, having been plagued with injuries at Arsenal. He came roaring back, which was great.
"And this young man has definitely got talent. He's got a bit of an injury at the moment. We're hoping that that will clear up shortly. And if it does, and I think it will, I'd love to have him."
