Amanda Ilestedt's 90th-minute winner saved the 2003 runners-up from embarrassment on Sunday against underdogs South Africa, who are ranked 51 rungs beneath them.
Asllani said while the effort was beneath Sweden's best, they were "more than satisfied" with the win in a wide-open tournament.
"This World Cup is harder to predict than any World Cup so far. There are so many teams that have developed greatly," she told reporters on Friday.
"I'm generally very impressed with the so-called 'underdog teams'."
Sweden have finished third on three separate occasions at the World Cup and are hoping to avoid heartbreak on the global stage yet again after a shootout defeat by Canada in the Olympic final two years ago.
Their opening effort in New Zealand was one they can build on, said coach Peter Gerhardsson, who focused the long break between matches on "tactical discussions."
He expects an unpredictable and physical Italy to keep them on their toes in Wellington after the 16th-ranked team beat Argentina 1-0 in their tensely fought opener in Auckland on Monday.
"They change around sometimes, adapting to the lineup of their opponents. They're also flexible sometimes in terms of the players they use. Some teams are sometimes easier to know (the lineup)," he said, via a translator.
Sweden beat Italy on penalties in their last meeting at the 2022 Algarve Cup.
"They had a lineup that we felt was somewhat adapted to our game plan, making it somewhat more difficult for us," said Gerhardsson. "It's a skilled team... especially bearing in mind that they are physical."
