He said if Umno leaders used a rough approach, it would only invite problems like former Terengganu menteri besar Datuk Seri Ahmad Said's reaction of quitting the party.
"If we had acted harshly, it would not be a problem for him (Ahmad) to leave Umno. It (situation) is not like in some states like Johor, where Umno is already in the members' blood. In Kelantan, is is difficult for party members to quit PAS or Umno as they have strong faith in their party.
"Both leaders (at the federal and state levels) must accept the fact that mistakes had been made by both sides," he told reporters after receiving an honorary doctorate in political development from Syarif Hidayatullah State Islamic University in Jakarta, Indonesia on Wednesday.
"It's their way, so we have to be careful as they can easily switch (party). It's their character."
Dr Mahathir, who is also former Umno president, said the political crisis in Terengganu arose because of the party's weakness.
"Umno is weak now. The feeling of (party members) is that it is focusing less on the problems of the Malay community but more attention being paid on opposition parties, the Chinese community and so on.
"Hence, there is dissatisfaction among the Malays. They support (Umno) not because of the leadership but because they dislike the opposition," he said.
Dr Mahathir said the Umno top leadership needed to understand the sentiments of the party supporters at the grassroots level to ensure continued support for the party, especially in facing the next general election.
He stressed that Umno leaders should not listen totally to the individuals around them, but should instead also listen to the grouses of members who always supported the party.
Dr Mahathir also noted that Umno had in many instances, made the same mistakes, but not many of its party leaders were brave enough to correct the mistakes, making the top leaders feel that whatever they do receives support.
"Umno seldom learns. I've said this many times before but they still don't realise it. We will lose (power) if Umno does not learn and repeats those mistakes," he said.