Three heavy defeats in two months, the most recent a 5-0 mauling by Liverpool at White Hart Lane on Sunday, resulted in the sack for Villas-Boas with his expensively-assembled team lying a disappointing seventh in the Premier League table.
Spurs were also thrashed 6-0 at Manchester City three weeks ago and suffered the embarrassment of a 3-0 home defeat by struggling West Ham United in October but Redknapp felt it was too early to jettison the young Portuguese.
"I think people are over-reacting too quickly," he told Talksport Radio on Monday. "You lose a couple of games now and you're in trouble, it shouldn't be like that.
"You either think somebody is good at their job or not and when you appoint someone you should give them time and let them do the job," added Redknapp, who is now in charge of Championship leaders Queens Park Rangers.
"It's far too early for people to start wanting to pull the plug on him. You've got to give him time and see what he can do," he said just before it was announced that Villas-Boas had been dismissed.
The 36-year-old looked a broken man on Sunday after his team, reduced to 10 men following the 63rd minute sending-off of Brazilian midfielder Paulinho, were led a merry dance by a Luis Suarez-inspired Liverpool side.
A place in the Europa League knockout stages and a quarter-final Capital One Cup date with West Ham on Wednesday were clearly of little consequence to a Spurs board that had splashed out more than 100 million pounds ($162.98 million) on transfers in the close season.
The Londoners looked bereft of ideas and desperately short of fighting spirit when they were ripped apart by Liverpool but, looking beyond that crushing defeat, Villas-Boas also failed to recognise the importance of the powerful British press.
The Portuguese known as 'AVB', who was also sacked by London rivals Chelsea in 2012 after moving to Stamford Bridge following a highly successful spell with Porto, never got close to the friendly rapport Redknapp shared with the media.
A reflection that the pressure was beginning to get to Villas-Boas came after a 2-2 draw with Manchester United at the start of the month.
The Spurs manager snapped at a reporter after he wrote an article suggesting that "any of us could have had AVB's success at Porto".
"You always chase people and attack people and you don't attack them from the front you attack from sitting down with the things you write," was Villas-Boas's retort.
"You attack integrity and competence when you don't even know that person. Only when I give you the chance (to meet me) can you reach conclusions like you did."
Villas-Boas's frosty relationship with the media began during his time with Chelsea when he was criticised for the manner of his attempted overhaul of the old-guard players at Stamford Bridge.
He was sacked in mid-season with Chelsea in turmoil but his successor Roberto Di Matteo turned the club around and went on to land a Champions League-FA Cup double.
Villas-Boas took over at Spurs in July 2012 and, under him, they achieved their highest-ever Premier League points haul.
In the close season, however, he had to rebuild the squad following the world record sale of dazzling Wales winger Gareth Bale to Real Madrid.
Twelve new faces were brought in and early results hinted at a possible Premier League title assault.
Results, and performances, have since unravelled and Villas-Boas has not helped himself with his monotone ramblings in news conferences and his often glum disposition. His handling of goalkeeper Hugo Lloris's concussion was also criticised.
However, it was the look of utter bewilderment on the face of chairman Daniel Levy that spoke volumes during Sunday's annihilation by Liverpool and it came as little surprise when Spurs wielded the axe a day later.
($1 = 0.6136 British pounds)