Foster thought the Pilgrims could take positives from drawing 1-1 at Leeds in the first tie, and achieving the same scoreline in the return match over 90 minutes before the visitors' strength in depth within their squad proved decisive.
Goals from substitutes Crysensio Summerville and Georginio Rutter, who cost United a club record £36 million from German club Hoffenheim in January 2023, either side of half-time in extra-time put them 3-1 up.
Argyle striker Ryan Hardie then conceded a late own goal as he tried to defend an inswinging corner from Ilia Gruev and the ball flicked off his head and into the far corner of the net.
Leeds had opened the scoring in the 66th minute when Wilfried Gnonto drilled a low shot past goalkeeper Conor Hazard but Argyle defender Brendan Galloway equalised with a close range finish in the 79th minute following a free-kick.
Foster said: "One thing we spoke about leading into the game was to come away from this with no regrets, and I'm proud of the way they approached the game, I'm proud of how difficult they have made it for Leeds over two games.
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