A handling error in the last minute allowed Liverpool to steal victory after Spurs had been the better side in the second half.
"Every time I watch Gazzaniga play, he's playing very well," Jenas told BBC Match of the Day.
"If you're Gazzaniga now, you're going: 'It's time for me to get my opportunity'. And I think he should do."
Gazzaniga, 27, has made 10 Spurs appearances this season, including two in the Premier League when Lloris was unavailable in September.
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