The Reds were edged out on away goals by Zenit St Petersburg despite a stirring comeback after falling 3-0 behind on aggregate early in the second leg of their last-32 tie at Anfield.
Rodgers had hoped to oversee another celebrated European comeback but, despite two fine free-kicks from Luis Suarez sandwiched in-between Joe Allen's effort, had to settle for glorious failure.
Despite the result eliminating the club's last hope of silverware this season and leaving them fighting to finish higher than their current Barclays Premier League position of seventh, Rodgers is not downbeat.
Rodgers said: "Our season doesn't finish, and never was going to finish, until the final whistle against QPR.
"This is a group that is growing all the time. You see the level of performance last night, to dominate a team of that ilk and control the game like we did was incredible really.
"For us, going forward, it is to continue with how we have been working since the turn of the year. As the season has gone on we have got better and improved.
"We want to carry that through right until the last whistle at the end of the season.
"You can see the players have the hunger and determination to do that. We will look to demonstrate that in the last 11 games."
Liverpool's hopes of overturning the 2-0 deficit from the first leg suffered a blow when a mistake from veteran Jamie Carragher - making his 150th, and as it transpired last, European appearance - gifted an early goal to £32million Brazilian Hulk.
But backed by a typically vibrant crowd, the Reds responded with Suarez quickly levelling on the night with a set-piece from outside the box and Allen tucking in a rebound after his own header was saved.
Suarez curled in a sublime second free-kick just before the hour but despite a host of other opportunities - and having a good penalty appeal declined - the Reds could not claim the other goal they needed.
Rodgers was sorry not to reward the crowd with the winner they craved but expects such an atmosphere to be recreated many times in the future.
Rodgers said: "It was absolutely breathtaking.
"One of the real values of this football club is unity - how everyone came together and we just missed out.
"But hopefully in the future there will be many more great nights for us to celebrate.
"Having sampled that as a manager, in the home dugout, to feel that - I want many more occasions like that and with bigger prizes.
"We really needed the supporters and they were right behind us all the way.
"I am just disappointed we couldn't do it for them, but hopefully there will be many more in the future when we can do it for them."
Liverpool are not in action again until they travel to Wigan on March 2.
Their remaining fixtures include home clashes with Tottenham, Chelsea and Everton but otherwise they face a host of teams currently in the bottom half.
Presently seventh, their challenge is to claw back a nine-point gap to fourth-placed Tottenham.
He said: "We need to do our best. We are out of the cup competitions and that is something we will look to put right going forward.
"We want to win trophies here, that is the idea.
"For the remainder of the season it is to finish as high up the league as we can.
"When I came here in the summer that was the priority given to me.
"There has been some great growth in the group and that will continue.
"We want to keep showing our quality of fight and spirit right the way through to the QPR game.
"Then we will reassess in the summer and we will be in a much better position come next season.
"The framework will already be in place. It is difficult for players with a new manager coming in, with different ideas and work.
"But I think we are now starting to see there is a flow in it.
"They are comfortable with it and we are scoring goals and producing performances. Hopefully we can continue."