"We were really comfortable from kick-off," he told the club's official website.
"We dominated the game, and I put a lot of the blame down to myself because I should have finished that chance at the end of the second half. It was an easy chance."
But Spurs stood firm to move up to second place in the Premier League table and Alli was delighted to put another three points on the board.
"We made it difficult for ourselves by not seeing the game out earlier but three points away from home is always a good result," Alli added.