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Chairman Alan Savage told BBC Scotland: "It feels fantastic. You could argue with being deducted five points when we were already deducted 15 [last season], but we were determined to do our best.
"Kel [head coach Scott Kellacher] put a great squad together and everybody worked really hard from top to bottom and it shows what you can achieve.
"We are driving the club forward and want it to be sustainable without Alan Savages. That will take a long time, but if a couple of American film stars want to come in, we will see."
Defeat leaves Hamilton, who were themselves deducted 21 points this season for breaking various SPFL rules, facing the play-offs to avoid a second successive relegation. Accies, who finished two points behind East Fife, play Forfar Athletic in the semi-finals.
Without the points penalties, Hamilton would have instead be facing second-top Stenhousemuir in the promotion play-off semi-final.
The part-time Warriors finished two points behind Inverness after a final-day 2-0 win at Montrose.
Stenhousemuir will instead face Queen of the South, who finished 13 points behind, after a 4-1 win over Alloa Athletic that lifted the Dumfries side above their hosts.
Alloa will take on Airdrieonians, who finished second bottom in the Championship.
Meanwhile, East Kilbride made it two promotions in a row with an emphatic 5-0 win at home to Clyde and will replace Kelty Hearts, who had already been relegated, in the third tier next season.
The South Lanarkshire side finish five points clear of Spartans, who drew 2-2 away to Stirling Albion.
Spartans will face Clyde, who had rested a number of players against East Kilbride in preparation for the promotion play-offs, in the semi-finals.
Forfar warmed up for their meeting with Hamilton by drawing 1-1 away to Annan Athletic and finish fourth, three points clear of Stranraer.
Bottom side Edinburgh City prepared for their Pyramid Play-off final against Highland League champions Brora Rangers with a 5-0 thumping of second-bottom Dumbarton.
Brora received a bye into the final after Lowland League champions Linlithgow Rose were denied a place in the play-off semi-final because they do not possess an appropriate Scottish FA licence.
