He told BBC Berkshire: "So many times in football you go home from a game and you feel frustrated. It really plays on your mind.
"But a night like this is what you dream of and why you play the game."
Reading also reached the last eight of the Cup last season, losing 4-2 to Aston Villa in round six.
That run included a 2-1 third round replay win against Liverpool at Anfield, but Mills said the victory at Goodison trumped the success over the Reds.
"The result at Anfield was huge, but as you go further through the rounds it gets more important because you're closer to the end," he said.
"I felt an excitement in the changing rooms before the game and the boys were just so fantastic - I'm proud of every single one of them."
But with the Royals sitting 10th in the Championship, six points off the play-off places, Mills said that their Cup run would not distract them from the league.
"We've had a lot of games in a short space of time but the boys keep finding the energy, keep digging it out from somewhere," he added.
"The fans might see us beating Everton and think we should be beating this or that team, but you have to understand the difficulties and the different types of play.
"It's a big game for us on Saturday [against Middlesbrough]. We have to pick up three points to keep in the hunt for the play-offs and we'll rest well and get ready for it."
Source: BBC Sport
Source: BBC Sport