Gloucester head coach Laurie Fisher appeared to suggest he was ready to resign in the wake of their 30-27 loss to Harlequins at Kingsholm.
The home side threw away a 12-point lead in the last nine minutes, effectively ending their hopes of securing a European Champions Cup spot for next season.
Afterwards Fisher wrote on Twitter: "Unbelievable capitulation. Clearly not good enough. My responsibility. Time to make room for someone else."
Gloucester were contacted by Press Association Sport and a spokesman said: "Gloucester Rugby are aware of the tweet but are not in a position to comment further at this time."
Australian Fisher joined Gloucester from the Brumbies in July 2014, and despite a frustrating domestic season they beat Edinburgh to lift the European Challenge Cup a year later.
But they are currently ninth in the Aviva Premiership having won just five matches all season.
Charlie Sharples scored two tries for Gloucester and David Halaifonua one, with Billy Burns converting all three, and adding two penalties.
When they led 27-15 they were in complete control, but careless errors and a yellow card for hooker Richard Hibbard presented the game to resilient Quins.
Director of rugby David Humphreys said: "It's a sense of frustration, anger and disappointment after those last six or seven minutes of madness.
"We led by two scores and had to get the basics right but our defence and set-piece went to pieces after we had controlled the second half.
"European qualification is still mathematically possible but we had to get four or five points today and we didn't so it's a massive blow for the squad, especially after a great win over Saracens in our last home game."
Gloucester conceded tries to Ross Chisholm, Charlie Mulchrone, James Chisholm and Tim Visser, with Tim Swiel and James Lang both kicking a penalty and conversion in their bonus-point win.
Despite leaving it late, Harlequins director of rugby John Kingston believed his team were deserved winners.
He said: "At the end of the first half we led 15-10, but we were much the better side and should have been further in front. They then had a good period but we came back strongly and deserved to win.
"We knew we had to control the environment today as the influence of the crowd is very important here. I thought we managed to do so, for which the leaders in our team must take great credit.
"We've taken 10 points from this group of four games and that's better than our normal tally during the international period.
"We've won nine and lost eight in the league and have a cup semi-final at Exeter next week so it's not all doom and gloom. We've kept our European Cup hopes alive as finishing sixth or maybe seventh will be enough to secure us a spot for next season."