Schalke director of sport Horst Heldt admitted the club could not be completely satisfied with their season, even after sealing the final Champions League place.
Needing only a draw to remain ahead of their opponents and take a place in the Champions League play-off round, Jens Keller's side prevailed, with a little luck, to fulfil their objective for the season.
Schalke were out of the running for a top-four finish when Huub Stevens was relieved of his duties just before Christmas.
Keller took over and last week was given a contract for the next two seasons, yet Heldt did not appear overly impressed with the season when he spoke to reporters at the Dreisamstadion.
"For many people, what's important is winning the derby (against Borussia Dortmund), while others are desperate for us to play in the Champions League," he said.
"Everybody has their own criteria of success. I think we've done all right.
"I would have preferred a higher league position - we finished third last season.
"Of course fourth is very, very important. I'm just going to enjoy the day and then we can look back on the season next week."
Captain Benedikt Howedes was rather more upbeat, telling the club website: "I think after a season like this, we can certainly celebrate with a few cold beverages."
Freiburg coach Christian Streich saw his team, which were expected to battle relegation, finish fifth and qualify for the Europa League, but he too was not satisfied.
"We made too many individual errors and conceded two goals because of it," he said.
"I cannot be happy about us finishing fifth because we've lost a game we should not have lost."