Umar said from the hadith:
"Both of you came to demand your shares from the property (left behind by the Messenger of Allah).” (Referring to Hadrat ‘Abbas), he said: “You demanded your share from the property of your nephew, and he (referring to ‘Ali) demanded a share on behalf of his wife from the property of her father. Abu Bakr (Allah be pleased with him) said: ‘The Messenger of Allah (may peace be upon him) had said: We do not have any heirs; what we leave behind is (to be given in) charity.’ So both of you (Ali and Abbas) thought him (Abu Bakr) to be a liar, sinful, treacherous, and dishonest. And Allah knows that he was true, virtuous, well-guided and a follower of truth. When Abu Bakr passed away and (I have become) the successor of the Messenger of Allah (may peace be upon him) and Abu Bakr (Allah be pleased with him), you (Ali and Abbas) thought me (Umar) to be a liar, sinful, treacherous, and dishonest. And Allah knows that I am true, virtuous, well-guided and a follower of truth. I became the guardian of this property."
If you are trying to argue through that hadith that Ali thought Abu Bakr and Umar as liar, sinful, treacherous, and dishonest, you actually have no case. If indeed Ali thought so, as exerted by many Twelvers, it was his initial thought and later admitted his mistake as proven from the hadith itself. Here is the proof:
We can read from the earlier part of the hadith, when Umar posed the very same hadith about prophets do not have any heirs, Ali (as well as Al-Abbas) admitted to the authencity of the hadith by saying "yes".
"Umar said: “Wait and be patient. I adjure you by Allah by Whose order the heavens and the earth are sustained, don’t you know that the Messenger of Allah (may peace be upon him) said: ‘We (prophets) do not have any heirs; what we leave behind is (to be given in) charity?’” They said: “Yes.” Then he turned to Abbas and ‘Ali and said: “I adjure you both by Allah by Whose order the heavens and earth are sustained, don’t you know that the Messenger of Allah (may peace be upon him) said: ‘We do not have any heirs; what we leave behind is (to be given in) charity?’” They (too) said: “Yes.”
By agreeing that the hadith is authentically from Rasulullah (saw) shows Ali's admission to the fact that Abu Bakr was speaking the truth. That is evident enough for his initial thought of Abu Bakr (as well as Umar) as liar, sinful, treacherous, and dishonest was a mistake by him.