Gordon Matheson also refused to answer questions on allegations the rug was pulled on the plans after the judging panel in the competition did not opt for his favoured design.
Mr Matheson described the process that resulted in the cancellation as "robust" and accused the SNP of wanting to spend up to £500,000 on a public consultation on George Square.
Mr Matheson and his Labour colleagues also voted against calls for an automatic public consultation on any new proposals for the square, which should materialise within the month.
The support came despite senior members of the Labour administration expressing disquiet over how the public were consulted on the plans.
He was speaking as a report on the scrapping of the plans to implement the winning design for a new George Square went before the authority's decision-making executive committee.
Mr Matheson was asked by the SNP leadership if he would "apologise to the public, officers, the judging panel and the architects for wasting £100,000 and the time of the 40 council officers who had been working on this at various points over the last six months".
He was also pressed over reports in our sister paper the Sunday Herald that he axed the contest because his favourite design was not selected and asked if he would meet the architect behind the submission chosen by the panel. Mr Matheson ignored the calls. He said: "We have listened to the consensus view which has come out from this robust process. We've been criticised for not listening and now we're being criticised for listening.
"We will now be bringing forward proposals for a substantial facelift."
Last night, SNP group leader Graeme Hendry said: "The lack of remorse for making such a mess of George Square suggests Cllr Matheson either simply doesn't care or thinks what happened was acceptable.
"The people of Glasgow don't think it was acceptable and his failure of judgment on this issue will be his legacy."
A proposal by the Greens calling for new plans to come with a consultation was voted down.