The Swans fell behind early on to a Fernandinho strike - the first Premier League goal of 2014 - but hit back before the interval through Wilfried Bony.
Laudrup's side were very much in the game at that stage, but conceded twice around the hour mark to Yaya Toure and Aleksandar Kolarov as the points started to slip away.
Bony netted a spectacular second to draw Swansea to within one of the visitors to the Liberty Stadium, but that strike proved to be too little, too late.
Laudrup believes there are plenty of positives his players can take from the contest, with the Welsh outfit having shown that they are capable of mixing it with the best in the business.
He told Sky Sports: "I think the first half we were excellent.
"Of course, conceding three goals against a team like Man City makes it difficult to win.
"I think the first half was excellent, we had more chances. They got the second goal, a deflection from Ashley (Williams), and the third goal really hurt us.
"We tried to come back, we had a chance, and then they scored the third one - quite soft really as we could have done much more in different parts of the pitch. It was really uphill after that.
"We tried but being the third game in just six days, and the fourth in 10, and to be down 3-1, we got the second goal but it was too late."