The Brazilian ace netted within 20 seconds of the encounter and in the process scored the quickest goal in Champions League history.
His strike provided the platform for The Gunners' 4-0 triumph over the Dutch outfit and Ljungberg, who was also on the scoresheet, revealed the early salvo was the key.
"We were lucky that we got a goal that quickly, that was important for us," Ljungberg told Expressen.
"It was a massive, massive win for us. We have got much criticism for our play on the road.
"Therefore, we wanted to show what we can do and now we have done that."
Arsenal's victory in Philips Stadion ended a run of eight games without a win on their continental travels and puts them within touching distance of the second round.
Ljungberg added: "There was much cheering and happiness afterwards in the dressing room. It was an important win for us."
Gunners keeper Rami Shaaban also acknowledged the importance of the win but admitted the side rode their luck in the first half.
"The chances are now big that we can go through," confirmed Shaaban to Sportbladet.
"We were a bit fortunate to lead at the break.
"Fredrik and I talked about how many matches there are all the time nowadays. We just have to go back to London to prepare for the next match."
