The Chancellor accused Labour of whipping up controversy because they had nothing else to say about the financial package - but declined to say whether he approved of the ad.
The image - which claimed the changes would "help hardworking people do more of the things they enjoy" - was unveiled by Conservative chairman Grant Shapps on his Twitter feed last night.
But it was widely mocked on the social network as stereotyping the working class, while Liberal Democrat Treasury Chief Secretary Danny Alexander described it as "extraordinary".
Shadow chancellor Ed Balls told BBC Radio 4's Today programme that Mr Osborne must be "frustrated that his head of campaigns puts out an advert patronising working people by saying they'll be happy with a Bingo tax and a beer tax. What nonsense that is."
A senior Conservative Party source said there was no question of the image being pulled, because it was not part of a campaign.
But they added: "We are quite proud of those tax cuts... We stand by what was said in that advert."
Mr Osborne told BBC Breakfast: "I think it's patronising to say that it doesn't matter what the price of beer is or it doesn't matter that we don't help our Bingo halls. Because three quarters of the Bingo halls in this country have closed in recent decades.
"These are important Budget measures, they are not the only Budget measures.
"This whole story... was whipped up by a Labour Party that didn't have anything else to say about the economy.
"We are communicating what's in the Budget. The more people hear about the Budget the more confident people can be that they are on the right track."
Mr Osborne also insisted he had played Bingo in the past.
The penny off a pint of beer and the halving of Bingo duty to 10% were minor measures in a Budget dominated by help for pensioners and savers.
But Mr Shapps attempted to give them greater exposure, encouraging people to "spread the word" on Twitter - leading to a series of messages ridiculing the advert.
Mr Alexander said it was "rather patronising" and "demeans some quite sensible things" in the Budget.
"There are good reasons to be supporting Bingo, there are good reasons to be encouraging our pub sector to be stronger - that's the analysis behind those measures," he told BBC 2's Newsnight programme.
"This language, well that's for Grant Shapps to justify."
Twitter was awash with spoof versions, which included whippets, references to healthcare cuts and legal aid.
The hashtag #torybingo was trending with suggestions for number calling including "Eton's Den number 10" and "Bullingdon mates 88".
The dispute over the advert distracted from Mr Osborne's radical reforms to tax rules on retirement pots and new-style flexible Isas.
Mr Osborne told BBC Radio 4's Today programme: "This is a campaign that has really been got up by the Labour Party who decimated the Bingo industry and put alcohol taxes up and up such that many thousands of people lost their jobs in the pub industry.
"So if they want to go on talking about what they did for Bingo and the pub industry, they can be my guest. But I would suggest they actually try and engage with the Budget because they haven't had anything sensible to say about it yet."
The Prime Minister's spokesman said David Cameron had "full confidence" in Mr Shapps.
"He thinks he is doing a very good job," the spokesman said.
But at a regular briefing in Westminster the spokesman was unable to say when the Prime Minister had last played bingo.
"I have never asked him the question," the spokesman said.
Asked whether the Prime Minister expected the duty cuts to be passed on to customers the spokesman said: "My sense is that people in those industries are very keen to attract punters."
Mr Clegg said the poster was "a bit silly".
Asked on his weekly radio phone-in on LBC 97.3 if it would be right to describe it as a "Budget for plebs", he told a listener: "It certainly wouldn't be.
"As it happens, I think Grant Shapps, I think the tweet was a bit silly, partly because actually the issues involved in this Budget were really quite serious, including, by the way, giving support to the bingo industry, an important industry, giving support to our pubs and so on.
"But there are just much bigger things at stake."