The Manchester City forward was one of the Three Lions' key players at the tournament this summer but harbours a sense of regret after the agonising defeat on penalties to Italy in the Wembley showpiece.
Asked about his feelings on the Euros, Sterling said: "Bit of both, you still have people saying congratulations or something and it's like… there's not much to congratulate as we didn't win.
"That's the great thing within the squad, we're not happy with doing well and putting on a show for the country, we genuinely wanted to come home with that trophy and that's the mentality in the squad now.
"It was class we went to the final but we want to win, we want to make history and I think that's the message since day one when Gareth (Southgate) came in."
Sterling, who scored three times during Euro 2020, also hailed Gareth Southgate for helping fans forge a connection with the national team once again after years of disappointment.
He told Sky Sports News: "From the moment he [Southgate] came in - he really tried to work on building that relationship with the media and the fans and I think he's done a fantastic job at doing that.
"I think the fans are reconnected with the players again and you can see it when you go into the games, the players feel loved.
"Going into the games, even in the summer, you didn't feel any pressure. People might say, 'You played every game at Wembley', but that's huge pressure as you're at home and people expect things from you."