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The former Kiwi all-rounder said that he doesn't know what will happen going forward but the only option was to just "keep going".
Conway broke his hand as New Zealand defeated England on Wednesday to reach the final of the Twenty20 World Cup.
Finch felt there was little to choose between Australia and New Zealand.
Tim Seifert will replace Conway in Sunday's final against Australia.
Virat Kohli will return to take charge in the second and final Test in Mumbai.
The bitter defeat reminded Hussain of England's stunning loss in the final of the 2016 World T20 against the West Indies at Kolkata's Eden Gardens.
Daryl Mitchell's unbeaten 72 and Jimmy Neesham's blistering cameo in Abu Dhabi led New Zealand to a dramatic five-wicket win over England as they entered their first T20 World Cup final on Wednesday.
Neesham gave a quiet reminder of the side's determination to erase past heartbreaks by winning the final.
Wednesday's first semifinal would be a rematch of the 2019 ODI World Cup final in which England triumphed on boundary countback rule.
The veteran opener played until the penultimate over and guided the Kiwis to a score of 172/5, which proved to be a winning total in the end.
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