Alli was handed the captaincy as Spurs took on the Hornets in Milton Keynes, in a game that was initially slated to be played at the club's new stadium.
Alli scored a penalty in normal time, cancelling out Isaac Success' opener, before Erik Lamela gave Spurs the lead. Etienne Capoue then took the game to penalties, where the England international scored the winning kick.
The 22-year-old grew up in Milton Keynes and found his footing as a player at MK Dons, and the midfielder was thrilled to be given the armband by Mauricio Pochettino on his return to his hometown.
"It was good, it was a little bit too big for me but it was a massive honour," Alli told Sky Sports on the captaincy.
"I spoke to the gaffer yesterday and he asked me if I wanted to be [captain] and it was a real privilege.
"I think it's important when we're out on the pitch that we know we need to have 11 leaders out there, but it was a huge honour."
When asked if he would like to captain the side more in future games, he added: "If you asked the boys about my speech before they might disagree, but I think I want to be a leader out there anyway and whether I've got the armband or not it's important that that is my mentality."
Alli won the penalty that he scored to level proceedings, with Watford defender Christian Kabasele sent off after felling the star.
Hornets manager Javi Gracia, though, insists that the club will protest the decision.
"It is hard to accept, first the penalty and then the red card - I don't understand that decision. I don't understand why the referee showed the red card," he said.
"I am very proud of my players. I think we played very well and I would like to respect the referee's decision and to support them because I know it is not easy.
"We tried to the end and competed against a very good Tottenham team, I am proud of my players. I would have liked my players to have the reward because in my opinion they have played very well."