Lionel Messi opened the scoring on Saturday afternoon, before Angel Lafita made it 1-1 at Camp Nou, but Alexis Sanchez looked to have given the home side the win on 67 minutes.
However, late drama ensued, as Lafita rose highest to head home deep into injury-time to salvage a point for struggling Getafe and all but end Barca's hopes of retaining their La Liga crown.
Martino said after the game: "It is not the desired end, is not a good season from a personal point of view, obviously neither for Barcelona, because it isn't what they are used to.
"It has been a difficult season, with many problems off the pitch. We have tried to get over them with football and we were alive in the title race, until today.
"A poor season wasn't what we expected. There was the chance of not reaching the goals, but not due to our own mistakes. Even less after the two previous games in which we had to make comebacks.
"Sometimes the chances are asked when one believes he deserves to reclaim them. And sometimes one feels that his job wasn't good enough and is not necessary to ask for a new chance, because he doesn't deserve it.
"I will analyse what I have in my head. I think that after today we have played everything we had to play for in La Liga. Despite what maths say, now we have done everything and in this competition we have fought until today.
"If we have been unable to win today, we don't deserve to have more chances in La Liga.
"The players know what is dividing the club and what is the choice. There is still time to tell my future.
"I do not like to avoid responsibilities and feel that I am responsible. During the season we had some shortcomings which we haven't resolved."