Barca needed to beat leaders Atletico at home in their final game on Saturday to secure a fifth La Liga title in six years but could only manage a 1-1 draw at the Nou Camp and finished three points adrift of the Madrid club.
Atletico knocked them out in the quarter-finals of the Champions League and they lost to Real Madrid in the final of the King's Cup, a disappointing return for the world's second-richest club by income that prompted Martino's resignation midway through a two-year contract.
"We have not achieved our objectives and we cannot be satisfied," president Josep Bartomeu said in an interview with Spanish television broadcaster TV3.
"We will go into a period with profound changes," he added.
"There are some players that will not continue but our philosophy won't change.
"There are some things that have been decided, we will announce them in the following days. We will continue with our concept of football."
With Martino gone, the way is clear for Barca to appoint Luis Enrique, who stepped down last week after a successful season coaching Celta Vigo, as the Argentine's replacement.
A former Barca and Spain midfielder, Luis Enrique was filmed last week by Spanish TV at his home meeting with sporting director Andoni Zubizarreta and he is widely expected to be named in coming days.
Luis Enrique took over from Pep Guardiola as coach of Barca's B team in 2008 before a brief and troubled stint at Serie A club AS Roma.
Celta hired him to replace Abel Resino in June last year and the Galician club have impressed under the 44-year-old, playing some of the most attractive football in Spain.
He is seen as a Barca insider who will remain true to the club's possession-based style with its focus on relentless attack.
His first task would be to ensure the squad, which has looked limited at times this season, is strengthened in the right areas.
Among urgently needed reinforcements are a goalkeeper to replace Victor Valdes, at least one centre back and possibly a tall centre forward who can cause problems to opposition defences at crosses and attacking set pieces.
"A cycle has ended and the reality is that we have to make changes," centre back Javier Mascherano, one of several players who may move on, told Barca's TV channel.
"The club will make decisions and will create a competitive team," added the Argentine, who played in midfield before moving to Spain.
"A unique era is over. That's why it hurts so much because you never want a good thing to end.
"I don't know what I'll do. I'm very grateful to the club and I'll leave the day they don't want me.
"At this point I don't want to talk about my future. The most important thing right now is Barca and our defeat."
Another important task for Martino's successor will be to ensure four-times World Player of the Year Lionel Messi gets back to his brilliant best.
Messi, who missed two months of the season with a muscle injury, looked strangely subdued in Saturday's La Liga showdown against Atletico and only showed glimpses of his scintillating talent last term.
The Argentine has agreed a lucrative new contract with the club that will reportedly make him the world's best-paid player and Barca will need him to perform next season if they are to regain their dominance in Spain and Europe.
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