Solskjaer saw his first home game in charge spoiled by the Hammers as goals from Carlton Cole and Mark Noble moved West Ham out of the bottom three at the expense of Cardiff.
Solskjaer bemoaned his side's poor first-half performance for the defeat, but was happy with their second-half showing even though they came away without any reward.
"I think you have to say I have a mixture of many different emotions," Solskjaer told Sky Sports. "The first half never got going because of injuries and they had a few players staying down and a bad one for Demel so we hope he is okay.
"I was surprised by our first-half performance because we have been so bright in training and the second half was more like it. That's the way I want my team to play.
"We should have defended better of course, we should been tighter up to the man, don't let Carlton Cole have a free run like he did, but that was our first half today, we just didn't perform to our level.
"Second half that's more like it - energy, enthusiasm, chances, big chances and we could have and should have scored a goal or two.
"Sometimes football is like that, you have 20 shots on goal, they have ten, you have two thirds of possession and they win the game.
"At this level you need to take your chances and they did to be fair."
The defeat was Solskjaer's first in his second game in charge to leave Cardiff in the drop zone, but he believes if they can replicate their second-half showing they can climb out of trouble.
"I never thought this was going to be easy anyway, you don't expect that in the Premier League, it is a tough place to work," continued Solskjaer.
"There are five points up to tenth and if we get performances like in the second half we will be getting points."