The Liverpool manager responded angrily to suggestions he may not be in charge next season after his side's disappointing Premier League campaign ended with a 1-0 defeat at Swansea.
Reports in some Sunday newspapers had suggested that Dalglish would leave the manager's position during the summer, with Wigan boss Roberto Martinez being tipped as the man to replace him.
After watching Danny Graham's 100th career goal condemn them to an eighth-placed finish, Dalglish was asked if he expected to be in the Anfield hot seat next season.
He replied: "I expect the owners to have more dignity and integrity than to believe a story in a newspaper.
"We won't run away from the points tally or hide or 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."