Sherwood took charge of his first game at the club in Wednesday's 2-1 League Cup loss to West Ham, following the departure of Andre Villas-Boas on Monday.
Despite the defeat, Dembele believes Sherwood would be a popular choice among the playing staff.
"It's difficult to say right now (whether Sherwood should get the job permanently) because it's just happened recently," he told The Guardian.
"I don't know Tim that well. But the way he talks and his manner... I think everyone likes this.
"Everybody is very positive about this. It's difficult to have one day and change everything. It takes time but I think we've already started to play quite well (against West Ham)."
Villas-Boas left the club following a 5-0 defeat to Liverpool at White Hart Lane, with Spurs seventh in the Premier League.
Dembele claims there is a feeling of guilt among the squad over the 36-year-old's departure.
"I think everyone feels guilty and that's a normal thing," he added.
"It's a team sport. It's not one guy that's responsible, everyone is responsible.
"We have talked among the team already and we said to each other: 'Now let's do it. It's everybody's fault. We are one team, all together.'"
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