The prohibition, which came in for the first time this year, helped produce a family atmosphere for the more than 40,000 people who packed the streets for the biggest-ever Tram Sunday.
Chairman Keith Yates said: "It was eight o'clock at night and we were removing signs and barriers and we were still getting people coming to us and saying it was a family-friendly day.
"It was the first time for a long time that everybody felt relaxed. Everyone was enjoying themselves. They didn't feel intimidated.
"The on-street drink restrictions played a big, big part in that, as did people's reaction to it. I was getting feedback during the day that everyone was compliant with the restrictions.
"Lots of younger people were coming up and saying they were really enjoying it – the intimidation factor had gone.
"Some people had come for four years but never brought their kids. But they went back and got them and stayed for hours."
In the past the festival has been troubled by exuberant drinkers outside pubs.
The committee is already looking ahead to next year's festival and planning a fresh drive for donations from local business who benefit hugely from the day.
Mr Yates said: "I have no idea how much money comes into the town but if you have 40,000 and each one spends £10 it's a big boost to the economy for that day.
"And some will be spending £50 or £60 on food and drinks for a family. It's a tremendous amount of money."
A few weeks ago the committee had publicised a £5,000 deficit but, Mr Yates said, there had been a response to that and the festival was now back on an even keel.
He said: "We had a good response.
"Obviously, some traders may not wish to share their profit but a lot of people do help.
"One pensioner gave us £20.
"There are people out there who want to see the festival go ahead as a great family day."