He said the Mr Mahama was receptive to his criticism in the build-up to the flagbearership contest which the ex-president won by 95 percent of the total valid votes cast.
"We are politicians and you have to be in this game for some time to know that anything is possible. Particularly in African because there is so much uncertainty," Mr Bagbin said in an interview with Citi FM.
"And so, as you go round trying to show who is a better candidate you will definitely disagree with the other contestant... Anytime you disagree, people say you are a critic and sometimes they even say that it is an attack on the person but that is what democracy is about. That is what competition is about.
"But, at the end of the day he knows me very well and he has worked with me for a long time and he knows I don't harbour ill-will or hatred and so he knew that what I only criticised to improve. So, he was quite receptive, we had a good chat and we know that with that culture we could do more for the party and this country".
Mr Mahama polled 213,487 votes representing 95.23% of the total votes cast to beat the six other contestants to lead the largest opposition party in the 2020 general elections.
A former Vice-Chancellor of University of Professional Studies; Accra (UPSA), Prof. Joshua Alabi came second with 3,404 votes representing 1.52% of the total valid votes cast.
The Second Deputy Speaker and Member of Parliament for Nadowli/Kaleo, Mr Alban Kingsford Sumani Bagbin came third, polling 2,301 votes representing 1.03% of the total votes cast.
Goosie Tanoh also came fourth with 2,091 votes representing 0.93%.
Ekwow Spio Garbrah, a former Trades and Industry Minister, polled 1,447 votes which represents 0.65% of the total votes.
Former Chief Executive Officer (CEO) of the National Health Insurance Authority (NHIA), Mr Sylvester Mensah, secured 934 of valid votes cast representing o.42 percent.
And Nurudeen Iddrisu, a businessman, placed seventh with 520 votes representing 0.23%