Redknapp clapped supporters and signed autographs in the dug-out, despite fears of a hostile reaction from Pompey supporters towards the manager who won them the FA Cup two seasons ago.
Former Pompey striker Jermain Defoe, however, was dismissed for a stamp on Aaron Mokoena after doubling Spurs' lead before the break, with Tottenham old boy Kevin-Prince Boateng pulling a goal back after the interval to set up a tense finale.
"There was no trouble," Redknapp said. "I sat among the fans and they were fantastic, so it all got hyped out of nothing."
With Pompey bottom of the Barclays Premier League and struggling since Redknapp's departure nearly a year ago, the Spurs boss was unsure about what reception he would receive.
"It was a difficult day," he admitted. "I couldn't believe what I was reading, I thought 'why?'
"The club did very well out of me. Other people leave football clubs so what have I done wrong? I didn't know what to expect because of the different things being said."
Ledley King opened the scoring just before the half-hour mark with a header, capitalising on indecision from David James, who returned from the knee injury that ruled him out of England's win over Belarus last Wednesday.
Defoe tapped in for the second but, after Boateng volleyed home, the England striker was dismissed for his clash with Mokoena.
"If he kicked him, for sure he should be sent off," Redknapp said. "I told him 15 times before the game not to react if he gets kicks. Sure enough that is what he did."