Hamilton head coach Stuart Taylor has been left angered by Morton's 96th minute goal in the side's 1-1 draw - as referee Steven Reid added more time to the game.
Lewis Smith's first half effort looked to have sealed three Championship points for Taylor's side, before Ugwu's header off a Jaakko Oksanen free-kick found the net.
Accies are seventh in the league following the draw. Hamilton's Mihai Popescu was stretchered off in one stoppage while two players were booked for time-wasting at Cappielow.
Taylor was perplexed as to why Morton were given a free-kick in the first place after a foul near the technical area. Two minutes of additional stoppage-time left him furious.
"It wasn't a free-kick first and foremost," said Taylor. "They then lump it forward. I felt like I was a kid again where I was playing until the next goal went in.
"I didn't see any injuries, apart from Popescu's. But to be honest, I don't want to come down to that level. It is what it is and you get on with it.
"I was told there was five minutes added on. But that's a get-out as they say at least five. We'll be professional and I'm not really interested in. We'll keep going."
Hamilton have taken four points from an available nine this week, having lost to Kilmarnock last weekend and beaten Queen of the South at home on Tuesday.
Arbroath at New Douglas Park comes next for Taylor and his side.
"It's not right and it's a sore one," added Taylor on the Morton draw. "It was (a dominant performance).
"I thought we did very well. We moved the ball well in the first half.
"We created chances and could have been more ahead. We didn't take them, which is something we need to look at. We were comfortable defensively.
"Wherever those minutes came from, they came from. I can't say too much as I don't want to get in trouble, but it's a sore one. There's nothing I can do about time being added on."
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