Antonio Conte's side are out of Europe after a 3-0 loss at Camp Nou which began with Messi opening the scoring in the third minute.
Conte said: "We have to try to do both. I don't know, we can only look forward, to try and fight for a spot in the Champions League and win the FA Cup".
Alonso bemoaned Chelsea's luck throughout the two legs, but noted that if the club want a chance to do better next year, they will have to play well over their last stretch of the Premier League season to ensure a place in next year's competition. "We respect Barcelona, they have great players and are a big club... we want do a flawless job to go through to the next round".
Chelsea went into the match knowing fully well that they must score at the Camp Nou for them to have the chance of reaching the quarter final after the first leg ended 1-1.
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He's massively passionate about football and he's overstepped the mark and shouldn't have reacted. The former player is heard to say "All right", before appearing to spit at the auto .
Chelsea goalkeeper Thibaut Courtois admitted that his mistake allowed the Catalans to take an early lead.
Asked why Chelsea have struggled for consistency, Alonso said: "It's hard, so many games this year and we have not go the deepest squad maybe, new players this year".
Speaking during BT Sport's coverage of the game, Ferdinand said of the first goal conceded by Courtois: "The goalkeeper has got to do better there".
Having now exited the Champions League, the fixture list is beginning to ease up for the Blues. It was a pity to go out especially after two good performances against Barcelona, but this is football and it is life. It's my weakest point between my legs.
"Now we have to face another competition and for this reason we must trust in our strength and try to move on".
"My only worry is to have the players in the best form for Chelsea, then it's up to the national team coach to make the best decision for their country".
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