Inside centre Ian Whitten scored Ulster's try while Paddy Wallace matched Paterson blow for blow also kicking eight points.
Replacement Ian Humphreys kicked a late penalty for Ulster but it was not enough to save their blushes, or avoid a tongue-lashing from their angry coach McLaughlin.
"In the first half we didn't turn our possession into points and again we paid the consequences," he said.
"We've got to look at it and say it's not acceptable, not good enough.
"Okay, we got a point but we really should have got the victory.
"Rory Best went off and we lost our composure and this group of players has got to take a big look at themselves and realise that we can't stop playing."