A 4-3 penalty kick defeat by Brechin City after a 3-3 draw and a 4-4 aggregate tie was enough for the Glebe Park men to advance to the play-off final against Alloa.
Hughes said: “I feel for the club and for the supporters. Raith are a Championship club who should be pushing towards the Premiership. I have to say that this is my lowest I have ever felt in football and I take full responsibility for what has happened.”
Hughes had arrived to replace Gary Locke in February with the Stark’s Park men sitting 11 points clear of bottom side St Mirren and four ahead of Ayr United.
An upturn in results was expected under the manager who had guided Inverness Caledonian Thistle to their Scottish Cup triumph in 2015. However, it never happened.
A failure to sign a goalkeeper to cover for injuries resulted in midfielder Ryan Stevenson deputising between the sticks in a 1-0 defeat by Ayr and a 5-0 reverse at the hands of St Mirren, after which Hughes very publicly blasted his players, as the Paisley men jumped above the Fifers in the penultimate game of the season.
A final-day win against Ayr ensured that automatic relegation was avoided and redemption was offered via the play-offs.
That was lost thanks to Andy Jackson’s penalty-kick winner which came 30 minutes after Brechin had thought they had already won.
The opening goal came in 51 minutes when home defender Jean-Yves M’voto mistakenly rolled a backpass into Ross Caldwell’s path and the striker slotted the ball away.
M’voto made amends when he headed in an equaliser and Raith fans felt that the game would now turn in their favour.
They were mistaken as six minutes from full-time M’voto slipped and Alan Trouten put Brechin ahead again.
Brechin looked to be through, but in injury time Ryan Hardie forced Graeme Smith into a save and Declan McManus cracked home the rebound.
Hardie slipped Raith into the lead before the end of the first half of extra time, but Liam Watt levelled when he curled home a 35-yard free-kick on 115 minutes to set up the shoot-out.
Raith’s Danny Handling, Jordan Thompson and Declan McManus all scored, but Hardie, Bobby Barr and Scott Robertson missed.
Willie Dyer, Trouten and Ally Love hit the net for Brechin and, despite misses by Watt and Paul McLean, Jackson stepped up to score.
Hughes, pictured left, added: “We have shot ourselves in the foot and I do not just mean today.”
Brechin manager Darren Dods said: “I do not know where my players found their energy from but I am delighted that they did.”
Alloa also secured their place in the final thanks to a 4-3 penalty-kick success after a 1-0 win over visitors Airdrie in their semi which finished at 1-1 on aggregate.
Trailing after Wednesday night’s first leg, the Wasps drew level thanks to Jon Robertson’s 25-yard shot five minutes after half-time.
Greig Spence missed a great chance to send Alloa through and penalties were called for after deadlock had set in.
Steven Hetherington missed for the hosts, but the Diamonds’ Iain Russell and Kieran MacDonald both erred from the spot and Calum Waters kept cool to send Alloa through.
Manager Jim Goodwin said: “It was disappointing that we never put the game to bed during the 120 minutes. However, I am proud of the fitness and commitment of the players.”
Airdrie manager Mark Wilson said: “It is a cruel way to lose, especially after all the effort the players put in.”