Steve Clarke's men conceded in the final minute against 10-man Manchester City at The Hawthorns before suffering a second dose of agony at Newcastle when Papiss Cisse condemned them to another 2-1 reverse.
Next on the agenda for West Brom is Monday's home meeting with struggling Southampton, live on Sky Sports, when Olsson hopes their fortunes will improve if they stick to their principles.
He said: "I'd rather be part of a team that is positive and going for the win.
"We got punished against City and Newcastle and, after a performance like on Sunday, you feel even more gutted to come away with nothing.
"Hopefully, next time we will be the team granted a little bit of luck."