Spurs were dumped out of the competition by Nottingham Forest, who won 2-0 against a strong line-up.
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The result leaves Spurs with only three avenues left this season to end a trophy drought that's lasted since 2008.
That could spell trouble for their chances of keeping five-time league-winning manager Conte, as well as club hero Kane, who, at the age of 29, is still trophyless in his career.
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talkSPORT host and Aston Villa's all-time top Premier League goalscorer Gabby Agbonlahor was surprised more wasn't made of the most recent loss, saying: "I feel like Spurs are getting away with it.
"Spurs fans would take Conte playing this type of football if he's going to guarantee a trophy but they're not going to win the Premier League, they're not going to win the Champions League, the FA Cup is much harder to win than the Carabao Cup.
"Last night was the perfect chance for them to get past a Forest team who made a lot of changes, they went strong Spurs, and they couldn't get it done.
"People will say 'why do you keep calling Spurs 'Spursy'' because last night was the perfect example of a Spurs performance, they had a chance to get through."
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And that could be an issue for their star player and manager, with Conte linked to a return to Juventus, while rumours of Bayern Munich making a move for Kane won't go away.
"I don't think Conte will be there [next season]," Agbonlahor added. "I don't think they'll win anything this season and then it's a big discussion about Harry Kane.
"I said before Kane wouldn't leave because he wants to become the Premier League's top scorer but surely he's thinking 'come on, we're not going to win anything here, I need to go somewhere where I'm going to win trophies, joke's over'."
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