Goalkeeper Jose Reina was sent off nine minutes from time for head-butting defender James Perch while £35 million striker Andy Carroll, who endured a miserable return to his former club, headed straight down the tunnel having aimed a volley of abuse at his manager when he was replaced two minutes earlier.
Reina will miss the FA Cup semi-final against Everton as a result of his misdemeanour, and his side now find themselves 11 points adrift of Newcastle and a point behind Merseyside rivals Everton in the race for sixth place in the Premier League.
Dalglish said: "We started well enough. We passed and moved and looked pretty threatening, but obviously, it ended up with a lot of frustration and disappointment.
"The frustration and disappointment resulted in the actions Pepe (Reina) took when he got a deserved red card. Also when Andy came off and went up the tunnel, he was disappointed with the way the game was going, not necessarily for himself, but for the team, and the frustration took him up into the dressing room.
"We don't have a problem with people showing their desperation or disappointment or frustration, but we need to channel it better than we have done."
Meanwhile, Newcastle boss
It was a day to relish for Pardew as Cisse, the man he bought for less than a third of what the club raked in for Carroll, took his tally to seven goals in as many games.
Pardew said with a smile: "His English isn't great - I think he's only had one lesson since he's been here.
"We had Africa Day at the training ground on Friday with the food, that probably helped him. He had some curried goat and maybe that was why he was fuelled up."
Asked about the vastly differing fortunes of Cisse and Carroll, Pardew said: "I felt for Andy, I did. He's a terrific lad and he's having a tough year. But he will come back.
"On our side of the coin, Cisse was terrific, and long may that continue."