Alli supplied the assists for Harry Kane's double at Villa Park, where victory sent Tottenham to within two points of leaders Leicester City, who take on Newcastle United on Monday.
A 2-2 draw against Arsenal last weekend was followed by a 3-0 defeat to Borussia Dortmund in the Europa League last-16 first leg at Signal Iduna Park on Thursday.
But the midfielder believes Spurs have shown the spirit and ability needed to be crowned Premier League champions for the first time.
"We know it's possible [to win the league] and we're in good form and we know how good we are as a team. We've got to keep the same mentality we have all season," Alli told Sky Sports.
"We haven't had easy games, the draw against Arsenal and then Dortmund, but we've been in good form.
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"We know how good we are as a team and we fancy ourselves against anyone. The boys really feel it when we lose so it's good to bounce back with a win."
Villa goalkeeper Brad Guzan made important saves in the first half to deny Erik Lamela and Kane, who appeared keen to remain grounded regarding his team's chances of finishing top.
"I think we played very, very well. Getting a goal just before half-time and then straight after put us in a good position," the striker added.
"We created a lot of chances in the first half, we probably should have done better with our finishing. Their goalkeeper pulled off some good saves.
"It's exactly what we wanted, we had to start the second half like we did the first and we managed to get the goal early on.
"We were solid until the last five minutes when they had a couple of chances, but on the whole we were solid and limited them.
"I'm delighted to get another two but the most important thing is the win. Every one of us is fighting and we're doing well.
"All we can do is concentrate on winning our games and we have done that."