Daniel Agger and Daniel Sturridge scored in the second half to give Liverpool a 2-1 win over Newcastle, who had taken the lead through a Martin Skrtel own goal.
Despite 26 wins and 101 goals, Liverpool had to settle for second after Manchester City got the last day win over West Ham they required to lift the trophy.
Liverpool were five points clear with three matches to go, but a home defeat to Chelsea - thanks partly to Steven Gerrard's slip - and a 3-3 draw with Crystal Palace handed Manuel Pellegrini's men the trophy.
But given that they finished seventh last season, Rodgers was happy to end the campaign just two points behind the big-spending champions.
"Congratulations to Manchester City," the Liverpool manager said.
"My overriding feeling at the moment is one of sheer pride for the players.
"We have finished the season winning 12 games out of 14, drew one and lost one.
"So the players have shown an incredible level of consistency and quality in that period, and obviously over the course of the season to finish second behind Manchester City.
"We would prefer to finish top, but we finished just behind them and that's a great mark of the progress we've made this season.
"We have just finished short, but we'll be back. The goal is to try to win the title next year."
Rodgers revealed he tried to inspire his team to victory with the words of a Reds fan desperate for the glory days to return to Anfield.
"I read a letter to the players on the first day of the season from a supporter called Ben," the Northern Irishman said.
"He talked about us getting into the top four and the pride he has in the club, and it said not to just think about fourth but to think about winning.
"Probably at the time the players and maybe the staff - we all thought the letter was a bit far-fetched.
"But I truly believed we could progress, and I read the same letter back again today and all the words that went back into the players' minds today were the same at the beginning of the season.
"I think the word now is belief - we now believe we can be up here challenging, and all the young players will be much better for that."
Liverpool were in danger of ending the season on a low.
At half-time City were 1-0 up thanks to Samir Nasri's opener while Skrtel had unwittingly shinned the ball past Simon Mignolet.
Rodgers admits he would have been highly-disappointed had Liverpool come not ended the campaign on a high.
"At half-time I said to the players 'listen, we can't finish the season like this'," Rodgers added.
"Because it has been a remarkable campaign for us and it would be sad for us and the supporters if we just went out with a whimper.
"The players showed real character to pick themselves up again."
Gerrard also refused to be downbeat at the final whistle.
The England captain is looking forward to playing in the Champions League next year and he is hopeful of putting in the same level of performance he has shown this year.
"I can certainly play at this level for another year, for sure, because I feel so fit and so strong - even though I'm getting on," said the 33-year-old, who scored 14 goals this term.
"But the idea for me is to carry on until my legs pack in. I'll know when the day comes but it's not here just yet."
Newcastle ended a roller coaster season in 10th position.
Manager Alan Pardew was annoyed with referee Phil Dowd for sending Shola Ameobi off for dissent and dismissing Paul Dummett following a late tackle on Luis Suarez.
Ameobi's red was the most bizarre of the two. The striker was booked for arguing with the referee just before the restart and he continued to shout at Dowd, which caused the official to send him off.
"I think what happened is he said 'if you carry on I am going to send you off' and maybe sarcastically Shola said 'are you going to send me off?' and he did," the Newcastle manager said.
"That is what Phil told me. He should have managed it better than that. It was a shame.
"I know Shola and he doesn't swear.
"It was sad because it might be his last match for us.
"How angry can you get if you don't swear?
"The Paul Dummett one was just a yellow card. Brendan agreed with me."
Fans have started calling for Pardew's head, but he insists he will be back next year, along with several new signings.
"In the first half of the season we were very competitive and had form for Europe," said Pardew, who was given a seven-match ban for head-butting Hull's David Meyler in March.
"But in the second half we weren't good enough. I wasn't good enough.
"I understand that I need to come back better and stronger next year and we will."
Source: PA