There were few chances in a match in which United full-back Rafael was sent off in the second half for a second bookable offence.
But Redknapp believed his side had the best of the chances, with strikes from Rafael van der Vaart and Peter Crouch, and insisted Tottenham were getting closer to matching the Premier League big boys.
Redknapp, whose side remain fifth, one point behind Chelsea in the race for the Champions League spots, said: "What it does is show we are not a million miles behind the other teams. We played United close, we battered Man City here first game of the season and drew.
"We have to believe we are not inferior to anyone. We are getting closer and closer. The top five teams are getting closer and closer. We are outsiders, but the favourites will be Man United still."
Source: PA
Source: PA