Multiple drivers had times deleted in Friday's qualifying, and that continued in the Saturday shootout after the white lines had been moved at Turns 12 and 13 – where many of the offences occurred – in order to protect tyres from kerb damage.
Along with Lance Stroll, Ferrari's Charles Leclerc was one of two drivers to receive a five-second penalty in the sprint event, which in his case dropped him from seventh to 12th in the final classification.
Four drivers received penalties in Sunday's Grand Prix, namely Pierre Gasly, Sergio Perez, Alex Albon and Stroll.
Vasseur insisted that the FIA should learn lessons after regularly experiencing similar problems at the Austrian GP.
"I would say that the biggest issue for me of the weekend is track limits," said the Frenchman.
"Because you know when you are going to Spielberg that you will have issues with track limits, and we had issues with track limits here, and you get the results two hours after the race.
"And when we came before the weekend, we told them exactly the same, that it will be a festival. And it was a festival.
"I think on top of this, the drivers at the end they perhaps lost a little bit of concentration, and some guys, the last 10 laps, they were doing strikes every single lap. But you can't blame them in this situation, we have to find a solution."
Vasseur stressed that it's hard for fans to follow what's going on.
"I think it's not even good for the show," he said. "At least on the pit wall, you have the number of strikes, you can follow the story, you know where you are and so on. But I'm thinking about the guys who are in front of their TV, they don't have the story about the strikes.
"And at one stage they see Gasly five seconds, Gasly 10 seconds, Gasly 15 seconds. We have to think also about this. I think that we can anticipate this kind of issue."
Asked if it was right that such a situation could occur given how much Qatar had invested in the Losail circuit and the event, Vasseur said: "I won't go on this field because I don't know who is responsible for this.
"But it's not just a matter of kerbs. It's the complete process, the layout of the track, the kerbs, what is after the kerbs. We have to find a solution.
"But as you said, and I don't want to go on this field and to speak about investment, but we are coming to Qatar, they are doing a mega effort to organise the event, and to have this outcome is for me is not at the level of the championship."
Vasseur said he supported the FIA response to the safety concerns over Pirelli's tyres, and which led to limited stint lengths in Sunday's race.
"I think the reaction was quite good," he said when asked by Motorsport.com about the measures that were taken. "At the end of the day, it's always for me safety first.
"And we were not sure [about the tyres], and to have this kind of reaction, we did a good race, it was a good show.
"And I would say that the reaction was very appropriate. It's a bit of a shame to be in the situation."
