The Steelmen trailed 3-0 at half-time after a catastrophic opening period which saw them lose goals by Bruce Anderson, Ross Callachan (penalty) and Marios Ogkmpoe.
Motherwell – who lost Stephen O’Donnell to a straight red card for the foul which led to the penalty – went 4-0 down to David Moyo’s strike before O’Hara pulled one back from the spot.
He said: “I can only apologise to the supporters for the first half performance but we can’t dwell on it.
"We are under no illusions that we need to get ourselves out of danger and we’ve got a big game next week.
“Everybody is hurting. There’s been a feeling of positivity around the place recently and I think today that completely contradicted that.
“The start was massive. We never really got a foothold in the game because you need to earn the right to play.
“I think Hamilton were physical from the offset and by the time we got started, we were a man and two goals down.
The versatile former Peterborough United player was making just his second start under recently appointed ’Well gaffer Graham Alexander after recovering from a concussion problem.
Despite his team’s poor day, O’Hara did well in a number of positions as the Motherwell boss had to change his formation after O’Donnell’s dismissal.
The Steelmen were vastly better in the second half but O’Hara admitted that they’d given themselves too much to do after that disastrous start.
O’Hara, speaking to Lanarkshire Live Sport, added: “It’s too large a mountain to climb and things just spiralled from there. It’s not happened recently to us recently, hopefully it’s just a blip and we can put it right.
“We’ve been on the other side of that this season up at Aberdeen.
"Obviously, from that perspective you’re really positive and can start enjoying the game but it’s a dark place on the flip side.
“The only people who can turn it round are the players on the pitch and that’s what the manager said at half-time.
"Although we were a man down, he said we needed to try and win the second half.”