But he said such tensions are commonplace and merely resulted from "personality clashes".
The Mail & Guardian interviewed Lekota after Cope insiders indicated he is still aggrieved by the choice of Mvume Dandala as the party’s presidential candidate.
The sources said while he pretended in public that he was over the shock, his anger is still being felt in Cope.
Denying he was bitter, Lekota said any new party inevitably has problems. However, he remarked that the decision in Dandala’s favour was taken in his absence.
"I think we could have managed the process better; the meeting went ahead and we had to join later," he said.
After the matter was explained to him, however, he accepted the congress national committee’s decision.
Lekota said when the meeting took place he "was already committed’ to campaigning in the Western Cape, Free State and KwaZulu-Natal. Media reports suggested he boycotted the encounter.
Lekota also conceded Cope is not entirely the party of his dreams, but added: "It’s developing … it will be a much better, oiled machine by the end of its first year."
Bringing together people from different political parties with different political cultures has also been a challenge.
A report presented at Cope’s Bloemfontein inaugural congress in December highlighted the challenge of "parallel structures" caused by lack of cooperation between Cope members from the ANC and other organisations.
Lekota said he will not leave Cope even if he is unhappy, as he believes the rifts will soon heal.
"The leadership is developing a collective culture of working as a team," he said.
He also said he will not go to Parliament, as he plans "to devote my energies to cultivating this organisation".