Graham left the Liberty Stadium on transfer deadline day to join Sunderland in a £5million deal, earning the move back to his native North-East that the striker craved.
Swansea were left with little time to find a replacement and two potential late loan deals, understood to be for QPR's Jamie Mackie and Sevilla's Spanish international Manu del Moral, fell through.
Graham was Swansea's top scorer with 14 goals last term, and had contributed a further seven this season.
But Michu's prolific form left the former Watford man frustrated at his lack of game time.
With him gone, Swansea only have Itay Shechter and Luke Moore as back up; the pair have managed just two goals between them this season.
But Swans manager Laudrup believes it was the right decision to let Graham go.
He said: "It wasn't that Danny was unhappy but it was a combination of going elsewhere to play regularly, and especially the chance to go back home, which was his desire.
"I told him it was okay and I understood, but he had to understand there was the economic side. Once the offer from Sunderland was good enough, Swansea as a club were happy and that combination made it clear it was a decision we had to leave him go."
The Dane also believes the failure to replace the outgoing forward will not prove costly.
"It gave us a problem because we did not want to buy anyone so we were only looking at loans," he said.
"We tried a couple of things. One of them was quite advanced and suddenly the president of the other club changed the rules and it wasn't possible to have a loan, only a permanent deal.
"You can always press the panic button just to bring someone in, but I don't think that was the case here.
"I still believe I have options in the squad. Danny is a good player, but remember he was not playing regularly.
"I still think inside the team, even with injuries, we have possibilities to have quite a competitive team.
"We have scored more goals than last season, we have others who have scored goals.
"You can never argue about numbers but we still have our top scorer. We have not sold Michu, we have sold a player who was on the bench.
"The other strikers haven't scored much but our midfielders and wide players have.
"If we had 20 points instead of 34, or had only scored 20 goals, maybe you would have seen two new centre-forwards here. But you have to analyse the team and the situation you are in."
Swansea travel to West Ham tomorrow looking to maintain an excellent run that has seen them lose just once in their last 11 games in all competitions.
But Laudrup is wary of the powerful striking options available to opposite number Sam Allardyce as the Hammers look to turn around a miserable sequence of one win in their previous 11 fixtures.
He said: "West Ham have a good team and if you let them play they have players who can play like (Mark) Noble, (Joe) Cole, (Matt) Jarvis and (Kevin) Nolan.
"Up front they have power with Carlton Cole, Andy Carroll and Marouane Chamakh, although he is a slightly different player.
"It's a team that haven't had a good run lately, it is an important game for them, they need to bounce back and we have to continue our good moment."
Laudrup also sympathised with 16-goal forward Michu, after he missed out on a place in the Spain squad to face Uruguay next week.
He said: "Spain have so many players. They have Alvaro Negredo, Fernando Llorente, David Villa is back and sometimes none of them play.
"We are talking about a team that can allow themselves to leave a player like Juan Mata out of the 22, that says everything.
"It would have been nice for Michu because he had a fantastic season. He has one small problem, he has a Spanish passport, any other passport and it might be easier for him."