Former Everton boss Moyes, who faces the mighty task of following in the footsteps of Sir Alex Ferguson at Old Trafford, was an interested observer as Swansea enjoyed an emphatic 4-0 Europa League win over Malmo at the Liberty Stadium on Thursday night.
The Scot will return to Swansea for his first game in charge of United on August 17, and he would have left south Wales with points to ponder after watching them hit the ground running.
There were two goals for record signing Wilfried Bony and a strike from fellow new recruit Alejandro Pozuelo, while Michu picked up where he left off last term with a typically composed first-half finish.
Allied to encouraging signs of an understanding forming between the Spaniard and Bony, there was an impressive performance from Jonjo Shelvey - another debutant - in midfield.
Laudrup hopes the chance for players to bed in during meaningful European fixtures will lead to a strong start domestically.
"It's great to play these two serious games before the league starts," he said. "It's great for us to play a very important competition rather than two friendlies. I was happy to start now because of this.
"We can use these games as preparation for the Premier League.
"We know cup competitions are important but the Premier League is our daily bread. It is where we want to be and it is where we want to consolidate ourselves as a squad and a club this season.
"The players know what we want to do, but for now we just have to think about the one game we have played.
"We have conceded only one goal in pre-season - that gives confidence to the team - and we have looked strong at set-pieces. That was one of our weak points last season and it looks like we are improving there."
Laudrup also praised the application of the players against the Swedes as they gave themselves a handsome lead to take into next week's second leg.
"They did not underestimate Malmo, they showed they really wanted to be in this competition," he said.
"You would expect that after 22 years without the club playing in Europe - and a lot of my players have never played in Europe before. It's important for them."
The Dane was relieved to pick up no injuries on the night, but admits winger Pablo Hernandez is a doubt for the second leg after suffering a groin injury in training earlier this week.
He said: "It's not serious but we have to see for Thursday, if not then he will be ready for sure when we play in the league."