Liverpool suffered frustration at the hands of struggling Wigan as Steve Gohouri equalised for the visitors to force a 1-1 draw at Anfield on Saturday.
But Gohouri equalised in the 65th minute from close range to deny Liverpool their best winning sequence in the Premier League since May 2009.
Liverpool striker Luis Suarez marked his first start since his 22.8 million pound (30 million dollars) move from Ajax by twice striking the woodwork, but the Reds couldn't find a winner as Wigan boosted their survival bid.
The hosts are unbeaten in their last six outings but Dalglish will view this as two points dropped against opponents who are fighting for their Premier League lives.
No player has illustrated Liverpool's transformation under Dalglish more than Meireles.
The Portuguese midfielder, signed by Roy Hodgson last August, went into this game looking to continue his incredible scoring form after his winner at Chelsea last weekend.
In contrast, Wigan's bright start was summed up by Charles N'Zogbia, who created space for himself before curling a ninth-minute effort wide from the edge of the area.
It was only after Hugo Rodallega's ambitious 13th minute overhead kick that Liverpool clicked into gear.
Wigan keeper Ali Al Habsi grabbed Dirk Kuyt's speculative 20-yard drive at the second attempt before Meireles broke the deadlock in the 24th minute with a thunderous volley from 16 yards after Fabio Aurelio's cross from the left.
Liverpool should have doubled their lead three minutes later.
Suarez caused the Wigan defence countless problems with his trickery.
And the Uruguay international made space inside the area before letting fly with a curling effort which hit the far post and bounced to safety.
Wigan had taken four points from their last two meetings with Liverpool and they finished the half strongly as Pepe Reina was forced to keep out a low free-kick by Honduras international Maynor Figueroa.
But Liverpool failed to kick on after the interval and paid the price when Gohouri struck from close range in the 65th minute after a Wigan set-piece.
And the home team's frustrating day was summed up when Suarez hit the bar with a 20-yard free-kick 13 minutes from time.
Source: AFP Global Edition