The work drew 43 complaints, with people complaining that it would cause offence, encourage cruelty to animals and was unsuitable for broadcast before 9pm.
The ad, by agency Wieden & Kennedy, depicts two young boys watching something off-screen.
The elder boy says: "Watch, watch!" and they continue looking before bursting into laughter. "Do you want to see it again?" asks the older boy. "Watch, watch!"
The camera shot changes to reveal a Hudl tablet playing a video clip of a cat attempting to jump from one roof to another; but it misses and there is an audible screech. On-screen text appears, reading: "Let’s watch... Let’s laugh... Let’s share... Let’s Hudl..."
The ad appeared on TV and during 'Sex Bomb' on Channel 4’s video-on-demand service 4OD.
Tesco refuted the idea that the ad would encourage cruelty to animals, pointing out that the cat jumped off the roof of its own volition and that the children’s laughter was a perfectly natural reaction to the mishap.
The retailer added that the footage had been bought from a company specialising in "cat funnies" and that the firm had been in touch with the owner of the cat and been reassured that the animal was uninjured by its fall.
Tesco did acknowledge the mischievous nature of the ad, but did not accept that it encouraged animal abuse.
Tesco defended the accusations of offensiveness on the basis that the action took place in a natural, relaxed and informal setting, and was meant to be amusing and encouraged sharing, learning and having fun with family and friends.
Clearcast told the ASA that when approving the ad it had noted the cat’s fall and the boys’ amusement, but decided that the footage "merely depicted normal feline behaviour, albeit slightly clumsy".
While the ASA accepted that the ad might offend some viewers, it considered that the work "simply showed the children's natural reaction to viewing a video clip which featured a cat misjudging a jump".
It added: "We noted that the footage did not show the cat being encouraged or forced to jump and we therefore considered there was nothing in the ad that could be emulated or that was likely to encourage cruelty to animals.
"We concluded that the ad did not breach the code and that it did not require any scheduling restriction."