"It's indescribable," Rosenberg told TV6. "It's so big that I'm almost taken by the moment. Maybe I'll understand it when I sit on the couch later. It's hard to understand, it's too much almost."
Malmo's 4-2 aggregate playoff victory ended a 14-year period in the wilderness for Swedish sides in Europe's elite club competition.
Trailing 2-1 on aggregate from the away leg, Rosenberg converted an early penalty to put Malmo in the driving seat, with Magnus Eriksson adding another shortly afterwards with a stunning volley from distance.
Rosenberg then administered the coup de grace late in the game, calmly and cockily converting a counter-attack that guaranteed the Swedes a place in the group stage draw, which will be held on Thursday.
The 31-year-old, whose retirement from international football was announced the previous day by Sweden coach Erik Hamren, has only recently returned to the country following a 10-year spell abroad in the Netherlands, Germany, Spain and England.
The last two years of his travels were spent unhappily at West Bromwich Albion, where he failed to find the net in 28 appearances for the English side.
He has rediscovered his confidence and his touch back in Sweden with table-toppers Malmo and showed the kind of sublime skill and intelligence that he is capable of against Salzburg.
His penalty after 11 minutes was hammered high and hard into the net, and his second in the 84th minute was a model of composure as he waited for the right moment before finding the target.
"I felt that he (the defender) was coming, sliding in, and I didn't want to miss. I was afraid that he would block the ball," said Rosenberg of his decision to take a touch in the box.
He then calmly waited for the goalkeeper to commit before cheekily finishing the move by rolling the ball into the net.
Not since Malmo's bitter local rivals Helsingborg qualified for the group stage in the 2000/01 season, have the Swedish champions made it through the qualifying rounds.
"Now we're there," a delighted Rosenberg said. "It's good for us, and good for Swedish football."
(Reporting By Philip O'Connor; editing by Toby Davis)
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