The 2012 Premier League champions' defence of their title came to an end on Monday night after Robin van Persie's hat-trick secured Manchester United a 3-0 win over Aston Villa and a 20th top-flight trophy.
United had used last season's title heartbreak, when they lost out to City on goal difference on the final day of the campaign, to help inspire this term's success.
And Milner is keen for City to adopt a similar approach next season as Roberto Mancini's side also aim to finish this term with a flourish by beating Wigan Athletic in the FA Cup final next month.
"It hurts," Milner told Sky Sports News. "Well done to Manchester United, they're obviously a strong team and the league doesn't lie, so they deserve the league.
"We're massively disappointed, but it fuels the fire for next season and we're desperate to go again next season to try and win it back.
"Hopefully we can finish this season with silverware."
The England international added: "We've seen how hard it is to retain the title and how much they (United) used that disappointment from last season to drive them on this year.
"They've been very good in the league, very solid and seem to grind out results every week. They've deserved it and we have to look at where we've gone wrong and try to put that right."
Pablo Zabaleta feels a lack of consistency has cost City, while Milner believes the failure to score more goals when dominating games has held the team back.
"There have been games when we have dropped points when we shouldn't have done," he continued. "There have been games where we've been well on top and not put teams to bed.
"When we've had that period of dominance in a game, we've not scored two or three more goals and that's maybe where we could have improved this year.
"But if you look at our defensive record this year, it's still very strong and as a team we've got to keep improving."