Spurs are currently battling for a top-four finish but had to settle for a point at the Stadium of Light, as Sunderland defended resolutely and limited the chances for Redknapp's men.
The Spurs boss admits he is disappointed his side didn't manage to secure the win, but felt there were plenty of positives to take from the display.
He told Sky Sports: "You just have to keep picking up points. We all want to win every game and we came here today thinking it was a game we could have won.
"I think we had enough about us to have beaten them today. It wasn't to be but it's another point and another clean sheet, which is important away from home."
Spurs are currently third in the Premier League table but they're only three points above Newcastle, who won at Swansea on Friday.
Redknapp admits Newcastle are playing well at present but the Spurs boss remains confident his side will secure a place in the Champions League next season.
He added: "They (Newcastle) have done great, they have been in fantastic form, but we are playing well. If you look at the last few games, we are in good form, we look solid."