John Rankin - one of eight players leaving Dundee United along with boss Mixu Paatelainen - has revealed the squad apologised to their manager.
Defeat by city rivals Dundee on Monday confirmed United's relegation from the Scottish Premiership.
Boss Paatelainen left on Wednesday after only seven months at Tannadice.
"It's been a hard time and again we apologised to the manager because I don't think it's been anywhere near acceptable," said midfielder Rankin.
The 32-year-old, who joined United in 2011, had issued his own statement of apology to the club's fans via social media for a season that started poorly under Jackie McNamara, who was replaced with the former Finland coach in October.
And he told BBC Radio Scotland's Sportsound programme that this had been echoed at the Paatelainen's final team meeting with his squad.
"When he spoke to us, he was very respectful in what he had to say and thanked the players," said Rankin.
"Obviously we are devastated because that's another manager we've let down this season.
"To win six games from 35 is horrendous by any standard. It's not something that a club of the stature that Dundee United has expects."
Not being offered new contracts this summer along with Rankin are forwards Florent Sinama Pongolle, Ryan Dow and Edward Ofere, defenders Guy Demel, Callum Morris and Euan Spark, plus goalkeeper Joe McGovern.
It is likely that others will be allowed to leave Tannadice should they find new clubs as chairman Stephen Thompson is keen to make sweeping changes and reduce the wage bill.
However, Rankin cautioned Thompson against offloading too many first-team players while appreciating the need for change at the club after a bitterly disappointing campaign.
"He's making plans, he's making them very early to his credit," said the former Ross County, Inverness Caledonian Thistle and Hibernian midfielder.
"I think the chairman's openly said he's got a budget that merits the top six and the club will be playing in the Championship next season.
"It will be up to the new manager that comes in to decide on who he wants to keep and who he wants to go from the players that he has at his disposal just now, albeit he'll have to build a full new squad because I think there's only 12 players under contract.
"They've got a lot of young talent. You look at your Scott Frasers, Blair Spittals that are there that have still got contracts at the club.
"Charlie Telfer's to come back and Charlie will probably feel he has got a point to prove having been sent out on loan.
"For me, the club needs to keep hold of the leaders.
"It's your big characters that you need, leaders on the pitch, people with experience that will lead those boys through."
Rankin reiterated that United must gain promotion back to the Premiership at the first attempt or risk a lengthy period in the Championship.
"If you go down to the Championship and don't bounce back up at the first time of asking, you can find yourself there for two, three seasons," Rankin added.
"Before you know it, it turns into six, seven and eight seasons.
"We've seen Dunfermline do it, we've seen Hibs do it.
"That can't happen at a club the size of Dundee United."