Kenny Dalglish has reacted angrily to reports he is set to leave Liverpool this summer after the campaign ended with a 1-0 defeat at Swansea.
And Danny Graham's 100th career goal condemned Liverpool to their worst finish for 19 seasons.
But Dalglish insisted he is going nowhere and said: "I expect the owners to have more dignity and integrity than to believe a story in a newspaper."
The performance of Dalglish, his staff and the club in general will come under scrutiny when he convenes with owners John W Henry and Tom Werner in the days ahead.
Liverpool have slipped to an eighth-place finish in the Premier League having won 14 of their 38 fixtures.
The defeat by Swansea capped a season of frustration for the Reds. Michel Vorm made one stunning save to keep out Andy Carroll's overhead kick and another low stop to deny the striker.
Dalglish felt his side had deserved at least a point, but acknowledged their campaign, which ended with Liverpool below local rivals Everton for the first time since 2005, had not been good enough. "I think on the second-half performance, the least they deserved was a point," he said.
"We've got to keep believing and in credit to the players they have kept believing. The passing and moving at times has been excellent and the goalkeeper's save to stop Andy was fantastic. We just have to keep going and maybe next year the luck will change for us.
"We won't say the points tally is satisfactory to anyone who works for or supports Liverpool Football Club. We will face up to reality. The performances have been excellent in a lot of cases but not the points tally, so we will try our best to correct that."
The Reds were without captain Steven Gerrard after he failed to sufficiently recover from a back problem.
But Dalglish is confident the midfielder will be fit to be part of the England Euro 2012 squad.
He said: "It's not my concern, but I wouldn't think he'll be a problem."
For Swansea the result capped a fantastic debut season in the Barclays Premier League, which has also seen them claim memorable wins over Arsenal and champions Manchester City. They missed out on a top-10 finish to West Brom on goals scored.
Manager Brendan Rodgers admitted the win had been the perfect way to cap the campaign. "It has been a fairytale and what an end to the season," he said.
"The players did brilliantly, their pressing and work-rate was phenomenal.
"Everyone associates us with our passing, movement and creativity, but behind it there is a real hunger to get the ball back and the hunger was incredible today.
"We were worthy winners and it finished a brilliant season. We have kept 14 clean sheets, which is outstanding at this level and to finish having beaten Arsenal, Manchester City and Liverpool in our first season gives us a big boost going forward."
The victory marked the final Swansea appearances for loan stars Steven Caulker and Gylfi Sigurdsson as they return to Tottenham and Hoffenheim respectively. But Rodgers is hopeful of bringing the pair back to south Wales next term, having reportedly had a bid to make Sigurdsson's move permanent rejected.
"The season has finished and it's about planning going forward. In football terms the squad will break up as players will leave and players will come in.
"I will speak to Tottenham on Steven Caulker, he has been incredible for me this season at just 19 years of age. With Gylfi, we will have talks with Hoffenheim over the course of the next week or so. That's the challenge for me, recycling the squad, retaining that hunger and giving the players help."