The First Minister paid tribute to the Glasgow club after a penalty shootout in Seville on Wednesday night saw German side Eintracht Frankfurt triumph.
During First Minister’s Questions in Holyrood on Thursday, Ms Sturgeon said the result was “heart-breaking for the team and their many, many fans”.
But she added: “The achievement of getting to the final was considerable, they played extremely well last night, it was a gutsy performance.
“So despite the disappointment the team, everybody associated with the team and the many fans in Seville and watching across Scotland will feel today, they should also feel extremely proud of their team.
“They did Scottish football and Scotland proud last night and I send them my congratulations for that achievement.”
Her comments came after former Rangers player Trevor Steven said the club had “elevated” the Scottish game with their run to the final.
Speaking on BBC Radio Scotland’s Good Morning Scotland programme, he said: “This run has been just absolutely mind-blowing, no-one expected Rangers to go this distance in the competition when you consider how it all started quite shakily really.
“For Scottish football, it has elevated the game in Scotland massively.
“When you consider the journey through the season to get to the final, and the euphoria it created, it was such a great experience for everyone.
“The lads should be absolutely proud of themselves, and the fans supported them brilliantly all the way through this tremendous run.
“To get to the end of extra time, and have the chances we had… that is probably the most galling part of it because it was so close to a victory and then goes into penalties, and anything can happen.
“Frankfurt are a good side, they are a well organised team. There is reasons why they put out Barcelona and there’s reasons why they put out West Ham.
“It was a tough 120 minutes and we weren’t quite at our best.”
After the final whistle blew in Seville, politicians from across the political spectrum praised Rangers for their performance as they commiserated with the team.
Scottish Secretary Alister Jack said the players had done “yourselves, your amazing fans and Scotland proud”.
He added it had been a “fantastic achievement to get to a major European final”, but “it just wasn’t to be on a hot night in Seville”.
Health Secretary Humza Yousaf – a Celtic fan – said the penalty shootout had been a “cruel, cruel way to lose it” but he added that the fans “should be proud of their team getting to the final”.
Sports minister Maree Todd said “defeats don’t come tougher than that”.
She tweeted: “The players will be devastated but there’s a lot to be proud of. Brutal way to end a well matched game.”
Scottish Labour leader Anas Sarwar praised the “tremendous effort by @RangersFC”.
He added: “While the loss in the final will hurt, they should be proud of the incredible journey.”
Scottish Conservative leader Douglas Ross tweeted: “Well played @RangersFC. Not the result you deserved but you did Scottish football proud this evening.”