Kobe have been struggling at the wrong end of the Japanese league standings for much of the season but put aside their poor form to hand Kevin Muscat's (49) Marinos a 3-2 loss at Saitama Stadium to secure a place in Saturday's quarter-final draw.
"We came here as underdogs, but I told the players that this didn't make things difficult," Yoshida said. "It meant we didn't have anything to lose.
"The players demonstrated that on the pitch and really challenged themselves in this game. From here I think this game will help us in the two possible games remaining in this competition and later in the league."
Kobe have struggled to establish themselves consistently among the elite of Japanese and Asian football despite the money lavished on the club by Hiroshi Mikitani (57), owner of Japanese online retailer Rakuten, for almost two decades.
They are currently third from bottom in the J1 League and have only one trophy - the 2019 Emperor's Cup - to their name despite regular high-profile signings from Japan and abroad.
Spanish World Cup winner Andres Iniesta (38) is Kobe's best-known player but his fitness has become less reliable, and injuries and poor form have meant other players have failed to step up to lead the team.
Constant changes on the touchline have not helped either, with Yoshida the club's fourth coach since the season started in mid-February.
Despite those issues, Kobe rose to the occasion against Marinos to put on an efficient and effective performance that moved them a step closer to the Asian title.
Kobe will be joined in the quarter-final draw by two-time winners Jeonbuk Motors after their 2-1 extra-time win over fellow South Koreans Daegu FC.
Hong Kong's Kitchee take on BG Pathum United from Thailand and Japanese side Urawa Red Diamonds meet Malaysian champions Johor Darul Ta'zim in the remaining Round of 16 matches on Friday, August 19th.
"It was a tough game for the whole 90 minutes but we got this result because we played as a unit offensively and defensively and worked hard," said Kobe captain Hotaru Yamaguchi (31).
"That really helped us to win this game."
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