Hearts boss Derek McInnes believes his team must "make it the norm" to be "challenging for trophies on a more regular basis."
Hearts were on the brink of winning their first Scottish Premiership title since 1959-1960, but lost on the final day to Celtic, who secured their 56th top-flight title with a 3-1 victory.
Lawrence Shankland gave Hearts the lead at Celtic Park, before an Arne Engels penalty was followed up by late goals from Daizen Maeda and Callum Osmand.
Since the start of October, Hearts spent 226 days at the top of the table, but Martin O'Neill's side got over the line on the final day of the season.
Celtic have now won 14 of the last 15 Scottish Premiership titles, while the last non-Old Firm side to lift the trophy was Aberdeen in 1984-85.
Despite their last heartbreak, McInnes believes it was a positive season for Hearts, who must now build on their second-place finish.
"In the cold light of day, when we look back, there's been so much positivity from where we were at the beginning of the season," he said after collecting the Scottish Football Writers' Association Manager of the Year award.
"The intention now is to dust ourselves down and try and enjoy our break, but be ready for the challenges ahead.
"I fully believe that those challenges are going to be met, with the enthusiasm from everybody at the club and the desire to improve and make it the norm for us to be challenging for trophies on a more regular basis."