With fellow A-League side Central Coast having played Nagoya twice in the Group Stage of the continental competition, it provided Kosmina the opportunity to seek out Mariners counterpart Graham Arnold for some additional insight on their Japanese opponents, as the Reds seek to qualify for the quarterfinals for a second time having reached the final in 2008.
Nagoya were lucky to leave the Central Coast with a point on Matchday Two after holding on for a 1-1 draw, but the J.League side fully deserved their place in the last 16 ahead of the Mariners after easing to a 3-0 win earlier this month.
But after Adelaide posted four wins and a draw to impressively top Group E ahead of Uzbekistan's Bunyodkor following a 2-0 win over Japan's Gamba Osaka two weeks ago, the Reds will look to make full use of home advantage at Hindmarsh Stadium to secure a place in next month's draw for September's quarter-finals.
"I watched them against the Central Coast last week and had a good chat with Graham Arnold the other day, and they are a good side," said Kosmina.
"They've got a couple of national team players and they played well, but having said that I think Central Coast could have got themselves back in the game after half time, and I think Arnie was probably disappointed with the way they conceded the two goals in the first half as well.
"Any of the Japanese teams are beatable, they've got to make the trip and these are all things that can help us get on with the job, but the fact is we've got to get our heads in the right space before we go out there and if we do that then I think we've got every chance of being successful."
Defender Jon McKain is fit to feature against Nagoya despite having a modified training workload due to a sore Achilles.
With Adelaide's last four competitive outings coming in the AFC Champions League following the end of the A-League season in the last week of March, Nagoya are in the middle of their J.League campaign and lost 1-0 at home to Cerezo Osaka at home on Friday.
Like Kosmina, Nagoya coach Dragan Stojkovic has no suspension headaches to deal with as the J.League side look to return to the quarter-finals after falling in the last 16 to Korea Republic's Suwon Samsung Bluewings in 2012 following their appearance in the 2009 semi-finals.
With Saudi Arabian trio Al Ittihad, Al Hilal and Al Ahli already assured of a place in the quarter-finals alongside Iran's Sepahan following their wins in the Round of 16 last week, 2010 champions Seongnam Ilhwa Chunma will look to seal their place in the June 14 draw for the quarter-finals when they entertain Bunyodkor on Tuesday.
Seongnam coach Shin Tae-yong, who saw his side draw 0-0 with Daegu on Saturday, will be without Vladimir Jovancic due to suspension after the Serbian striker scored twice two weeks ago as the 2008 semi-finalists secured top spot in Group G with a 3-0 win over Tianjin Teda in China.
Uzbekistan champions Bunyodkor, meanwhile, are looking to return to the quarter-finals for the first time since 2009 having lost in the Round of 16 in the last two seasons - to Saudi Arabia's Al Hilal in 2010 and Iran's Sepahan 12 months ago.
Mirdjalal Kasimov's side secured their place in the last 16 for the fifth consecutive season two weeks ago as Anvar Gafurov's header at the start of the second half proved the difference to edge out Pohang Steelers 1-0 in Tashkent to advance at the expense of the 2009 champions.
The quarter-final line-up will be completed on Wednesday as Emperor's Cup winners FC Tokyo travel to take on Chinese Super League champions Guangzhou Evergrande, while Ulsan Hyundai entertain J.League champions Kashiwa Reysol.
Tuesday's AFC Champions League Round of 16 Fixtures
Adelaide United vs Nagoya Grampus
Seongnam Ilhwa Chunma vs Bunyodkor
Wednesday's AFC Champions League Round of 16 Fixtures
Guangzhou Evergrande vs FC Tokyo
Ulsan Hyundai vs Kashiwa Reysol