Carroll stormed down the players' tunnel after being hauled off by Dalglish midway through the second-half, while Reina was dismissed for headbutting James Perch late on.
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."