Manchester City, who were eliminated in the opening round last season by Atletico Madrid after reaching the semi-finals in the two previous campaigns, will be the first side Lugano have faced in the Champions League.
Canada international Beckie said the tie poses a “big wildcard” but they have “done their research”.
The striker, who is yet to play in the competition having been an unused substitute in the first leg last season before missing the second because of international duty, said their early elimination 12 months ago has galvanised the side.
“It didn’t stain the season but it was disappointing and it is definitely motivation to not let that happen again this year,” Beckie told BBC Sport.
“We had great year last year, two trophies was more than anyone in England could say. But I think we have a group of girls that can really push in the Champions League.
“Part of the reason I moved here is so I could play Champions League. It is an exciting time in my career and hopefully we can have some success.”
In a week that Nick Cushing’s City side smashed the record for the biggest WSL crowd, with more than 31,000 watching them triumph against Manchester United at the Etihad Stadium on Saturday, Beckie said no-one has been distracted from what is being demanded on the pitch.
“It was a great occasion, a memorable and historic game for the club that a lot of us will remember for a long time,” she added.
“The girls did a good job managing the emotions of a big game like that.”
“From our performance there are a lot of things that we would like to do better and work on for out next game, and this is our goal.
“We just want to win and believe we are a team that should win and dominate teams – that is our mindset.”