David Moyes' side warmed up for Tuesday's Champions League clash away at Olympiakos with a hard-fought 2-0 victory at Selhurst Park through a Robin van Persie penalty and a fine strike by Wayne Rooney.
The victory sees them go within touching distance of fourth-placed Liverpool, but Sky Sports expert Redknapp says United's team is not as strong as their rivals at this moment and needs more time to gel.
"It's eight points and there's a long way to go. Liverpool have to go to Old Trafford as well," he told Saturday Night Football.
"Anything can happen, but I think with the way Liverpool are playing at the moment and their confidence, they do look like they are ahead of Manchester United at this stage in every department.
"I still feel there's a lot more to come from United and they are finding their way in terms of the relationship between Juan Mata, Rooney and Van Persie.
"I don't feel it worked perfect today, but there were signs. It was a big result for David Moyes."
The home side looked strong in the first half, but the game turned in the 62nd minute when Marouane Chamakh fouled Patrice Evra to concede a penalty.
Palace enjoyed more shots on target than the champions and Redknapp praised their approach to the game - but said United's confidence visibly grew when they got their noses in front.
"The first goal for Manchester United probably came after the best passage of play by Crystal Palace," he added.
"They had corners and balls in the box and it was one lack of concentration by Marouane Chamakh that cost them.
"David Moyes will be delighted. Tuesday is a big night at Olympiakos and it's game by game for Manchester United. They need a bit of confidence and that's exactly what this will do."