For their 6-0 FA Cup win over Millwall, Kane limped off just 10 minutes into the match with an ankle injury.
Alli told BBC One: "It is always horrible to lose a player like Harry, he's been in top form, but I think that shows our depth in quality and everyone stepped up a gear.
"It was an important win for us, not just for the cup but for the league as well, it was important that we kept the form and get in the goals.
"We are just hungry for goals and we knew it was going to be a difficult game and didn't want them to get back into the game because they did have a threat.
"But like I say, everyone wants to score and I think this is a good thing for this club."