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Adam and Skrtel were both dismissed for two bookable offences either side of half-time and Liverpool conceded three times after the red cards.
Adam walked after a lunge on Scott Parker and Spurs manager Harry Redknapp said he had no sympathy for Skrtel after his reckless challenge on Gareth Bale while he was on a booking.
Yet Dalglish insisted the needless dismissals do not point to indiscipline in his team.
"We have a very good record for discipline," Dalglish said. "That's why it's best left unsaid because it takes away from a very good performance from Tottenham.
"We will look at the video and if there is something wrong we can correct it. But you never saw Liverpool players running to the referee to dispute a decision, so there is no discipline problem."
Spurs took the lead in the seventh minute as Luka Modric scored his first goal since making it clear he wanted to leave the club before the season started.
After the red cards, Spurs ran out easy winners through Jermain Defoe's strike and Emmanuel Adebayor's two goals on his home debut.
"We started the game short of the level we have been recently," Dalglish added.
"They started better than us and obviously Modric scores a great goal and got them in front, Daniel Agger gets injured in the process and it's a great finish. It was the start of our downfall.
"It gave them an input into the game and despite the other incidents, which are best unanswered, we look at ourselves and what happened at the start of the game."
Former Arsenal striker Adebayor was delighted to mark his home debut in emphatic fashion.
The Togo star, who had already scored against Wolves on his first appearance last week, insisted he was never worried about the reaction from Spurs fans after his time with their north London rivals.
"I knew the fans already love me because that is what they are looking for - for players to score goals. Hopefully I will keep the hard work going," he said.
"I think a lot of players and teams will think Tottenham have a good squad and individual players and it will be tough now because people know what we can do. We have to find the solution."
Redknapp was delighted with his striker, who has now scored three goals in his first two games.
"Emmanuel Adebayor can play with anyone," he said. "He's trained like that, flying in training like he's going to run out of petrol, like someone's wound him up. He's always got a smile on his face, lets hope it continues."
Redknapp also praised Modric and hopes Spurs chairman Daniel Levy can agree a new deal with the Croatia midfielder after holding off Chelsea's bid to sign him before the last transfer deadline.
"Luka's is fine now, he's just getting on with it," he said. "I think the chairman will sit down with him and discuss his contract. That's what I'd like to happen.
"I hope he wants to stay, but I haven't discussed it with him.
"He plays with a smile on his face. That's why we were offered 40 million because he's a top player. That's why they want to pay that money because they've seen that before. He's a top, top player."
