Steve Clarke's side were in the mix for the top four in the early going of the campaign, but ultimately fell away - although eighth represented the club's highest league placing for 32 years.
However, the Sweden international does not believe he and his team-mates are ready to challenge the bigger clubs in the English top flight just yet.
"Last year we finished first of the teams we can compete with on a realistic level," he told the club's official website.
"It’s not realistic for us to compete with those top seven teams over a whole season.
"If everything works out it might be possible but it’s a difficult task to compete with those seven clubs over a season because their budgets are so much bigger."
The 30-year-old defender will be hoping to take advantage of a fine rest in the close-season, after admitting he had struggled to keep the pace last term.
Olsson represented his country at UEFA Euro 2012, going on to feature in all but two of West Brom's 38 league games, completing 90 minutes in all his appearances.
"I did feel towards the end of the season that I needed a break – I felt tired," he added.
"There were a lot of factors; first of all I’m not that young anymore, secondly last summer I had no break.
"The last part of the season was therefore not the best for the team - and me personally.
"I played a lot of games and only missed two Premier League games."