Manuel Pellegrini's side will be buoyed by that performance and the fact Tottenham played a high intensity game against Manchester City on Monday night.
But many feel Mauricio Pochettino's desire to end Tottenham's trophy draught could see him field a stronger side than expected.
Sky Sports pundit Charlie Nicholas is still backing West Ham to win a place in the quarter-finals, though, because he feels the Carabao Cup simply isn't a big enough carrot for Tottenham.
"It's a tough one for him (Pochettino) now as even winning this competition won't really prove anything as he's lifted Spurs to challenging for the title and playing in the Champions League," Nicholas told Sky Sports.
"I still think West Ham are improving generally and they're another team who should be going all out to win this thing so because of that and the changes Spurs will have to make, I think the Hammers can get through."
Nicholas has backed the Hammers to triumph 2-1 but his comments make for interesting reading.
While it is a backhanded compliment to Spurs that they have much bigger aims than lifting the league cup, Spurs also need to be mindful that this is the only trophy they have won in the last 30 years.
The former Arsenal and Celtic star has also called it right about West Ham, insisting they should be taking the competition seriously.
While injuries and suspensions will put paid to any hopes Pellegrini has of fielding anything like his strongest side, West Ham simply have to go for it to end their own trophy draught stretching back to 1980.
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