"It was a really good day and the atmosphere was unbelievable," Downing told the club's official website. "We played some great football.
"We have to take that into next season, performances like that, on the front foot, pressing teams. Spurs have got some unbelievable players and on Saturday we pressed them and they made a lot of mistakes. That's got to be the platform."
West Ham conclude their Premier League campaign next Sunday when they face Manchester City at the Etihad Stadium.