The hosts looked to have secured all three points after pulling back from being a goal down but a fine Simon Cox strike nine minutes from time ensured that both sides left with a point apiece.
However, despite it proving a hammer blow to Spurs' chances of securing a top-four spot, Redknapp has come out defiantly, claiming that his side will not let their heads drop as they look to keep up the pressure on Manchester City in the fight for a Champions League place.
He said: "We won't be deflated by the result. It's not the end of the world, everybody has results like that.
"We had the game in the bag and then the kid hit a worldy [shot]. It was unreal. He could try that every day for the next six years and he would not be able to do that again.
"We belong in the top four. We battered Man City on the first day of the season and couldn't get the win. We can give anyone a game. We've drawn with the top teams but they were games we could easily have won."
The Spurs manager also lamented City's spending power and admitted that it was difficult for his club to keep up with those around them.
He said: "We pushed Man City all the way. At the start of the year I thought Man City would win the league.
"I saw them bring in Yaya Toure and David Silva and all these people. I thought 'bloody hell!' All these people were world-class and mega in terms of cost and wages. Then they brought Dzeko in for £28 (€31.6) million."
"It's hard finding top players. Clubs want crazy money. We enquired about [Giuseppe] Rossi, and they were saying he's worth £35m (€39.5m). Crazy money. Way beyond what we can pay."