Cardiff, who missed the chance to record the first league double in this fixture, have now lost four of the five league games Solskjaer has taken charge of.
They remain 19th in the Premier League table, three points adrift of safety and with an inferior goal difference to all the sides above them.
"As anyone with Cardiff in their heart knows, there is nothing worse than losing this game.
"Every goal there is something you can point your finger at. The first goal was disappointing as we were just a split second late in all our decisions. That sets the tone for the rest of the half."