The Swedish side were viewed as potentially tricky opponents for the Swans having thrashed Hibernian 9-0 in the last round and with their domestic season in full flight.
But they were brushed aside by the Welsh club as Michu, record signing Wilfried Bony (two) and Alejandro Pozuelo found the net to complete an emphatic third qualifying round first leg win on the Swans' return to European competition after a 22-year absence.
"I am very pleased, perfection does not exist in football but it is very difficult not to be satisfied," said Laudrup.
"Four goals and none conceded against an opponent who were match-fit.
"There were also two goals for a new striker, and we know goals are so important for players up front.
"Pozuelo also scored in his first game, Michu is back scoring and we had no injuries so it is difficult not to be pleased."
Laudrup was pleased to see £12million man Bony break his duck at the earliest available opportunity, and promising signs that the Ivory Coast striker is forming a potent partnership with Michu.
"Michu and Bony have only played together in the Reading friendly," he said.
"But we had other new players. Jordi in the back, Jonjo in midfield plus Pozuelo and Canas.
"If we win 4-0 and the players don't know each other that well then it's not bad."
He added, referring to Bony's contribution: "For every forward it is important to score goals early when you join a new club, especially when he has a price tag on him.
"They were two different goals and I'm pleased for him."
But Laudrup did sound a note of caution ahead of next week's second leg in Sweden, and reminded his players the job is not done yet.
He said: "We have to finish this one in Malmo and I'm confident that we will then we will play in the next round.
"There is always a way back. I'm confident our approach will be exactly the same for the next game. The attitude of the players shows they really want to do well in this competition. We want to go as far as we can.
"I have to admit we are very close to getting through to the next round. But there is 90 minutes left to go."
Malmo boss Rikard Norling admitted his side had been second best, but felt the game had turned in Swansea's favour when Magnus Eriksson had a penalty appeal turned down after a challenge by Amat with the score at 1-0.
Norling said: "They are a good side, we knew that and we felt it during the game. We were solid during the first half but we lost our way a little bit because just as the momentum was starting to come our way they got the goal.
"The second half we had the penalty situation and we turned the ball over and they scored. It was a vital moment and it went to their side.
"I heard afterwards it looked like maybe it was a penalty but it is impossible for me to say if it was or was not."