"Love makes us patient. So many times we lose patience, even me, and I apologise for yesterday's (December 31) bad example," the Pope was quoted as saying by a media report.
One Twitter user posted the video clip of the incident and wrote: "I think his reaction was appropriate. #PopeFrancis #popeslap."
One user posted a meme showing the woman as year 2019 and Pope as year 2020. She wrote: "Let's start the new year like #PopeFrancis did!"
"You had one job #PopeFrancis," wrote another user.
One supporter had this to say: "I'm sorry but that woman was doing too much... plus, it was only a little pop... be easy on A@Pontifex #PopeFrancis."
One user posted a sarcastic post: "Look at this white old man smacking a woman's hand for wanting to shake his hand. You can tell that this incident clearly proves that he's a man of great patience & acceptance. Not to forget that the look of pure rage on his face which clearly shows his unconditional love. #PopeFrancis."
One Twitter user posted another clip of the Pope allegedly withdrawing his hand as the faithfuls kneel before him and try to kiss his hand.
"This is funny & WEIRD!! It's a custom to shake & kiss Pope's hand BUT Pope Francis seems DISGUSTED with the ceremony & yanks his hand away!! Least he can do is smile kindly & bless but see his attitude!! It's like he's saying 'Get on with it you low life'. #PopeFrancis #popeslap."
An otherwise serene Pope Francis had lost his cool momentarily on New Year's eve when the woman devotee had pulled at the pontiff's arm while he was greeting the faithfuls in St Peter's Square here.
As the 83-year-old Pope turned away after greeting the pilgrims standing behind the barricades along the kerbside to have a look at the nativity scene at the St Peter's square on December 31 night, the woman caught hold of his arm and pulled him close after he had extended his hand towards her.
A visibly annoyed pontiff gave a couple of light taps on her arm to get himself freed from her grip, even as his security personnel and accompanying officials intervened. The Pope looked upset after the incident as he walked away from the crowd.
( With inputs from IANS )