Spain, France and England have captured the spotlight in Switzerland, yet Sweden advanced to the quarter-finals with three impressive performances, including a decisive victory over Germany, finishing Group C with a flawless nine points.
"I feel like Sweden often goes unnoticed," attacking midfielder Asllani told reporters.
"And this situation somewhat benefits us because we genuinely believe we are among the top teams in the world based on our results in recent tournaments.
"However, people seldom mention us as a contender for the gold medal.
"We know we can triumph over any team when we perform at our best. We try not to dwell on it too much, but I think we deserve more discussion."
Sweden will face England, who secured second place in Group D, in Zurich on Thursday, recalling a 4-0 loss to the Lionesses in the last Euros three years ago.
However, Asllani mentioned that she and her teammates are concentrating on two recent draws against the reigning European champions as they pursue their first major title since winning the inaugural Euros in 1984.
"We have tremendous faith in each other and in the entire team. We play very intense and physical football, and since (coach) Peter (Gerhardsson) took over, that aspect has evolved," added Asllani.
"We have made significant progress over the past few years. Our players are at prominent clubs, and then we come together here. We are a very ambitious team seeking success."
She expressed her belief that the tournament truly begins with the quarter-finals.
"It feels like the tournament really kicks off once the group stage concludes. We have experience in these types of matches, and the excitement starts now... as you test your skills against the top teams."