The west Londoners were put to the sword by two early goals from Luis Suarez before Daniel Agger's header effectively ended the contest before halftime.
Although Redknapp admitted the two sides were on "a different level" throughout, he is certain the Rs can retain their top-flight status.
"I think we'll stay up still," Redknapp told reporters. "You'll all think that I'm mad, but I think we'll stay up. I only want positive people around me. I said that in the dressing room. Those that are moping around, the subs who don't play, they're not playing because they haven't been no good. If they was any good I'd be picking them. I look at miserable faces, I don't need them around me, I need people who are upbeat.
"The next couple of games are unbelievable. Chelsea away, Tottenham at home - two of the best teams in the country. Difficult games. We've got to keep going, but I still think we'll do it."
The manager went on to say that it was hard to understand why a team with the quality his has can be so thoroughly outplayed.
"It's hard. With the quality that we have everywhere. It was a difficult day," he said. "You look at the quality of their players - one club has spent nearly 200 million pounds on players and it was hard - we couldn't get near them. In the first half hour we were all over the place, they ran us ragged."
Redknapp also conceded that there are no quick fixes for the Loftus Road outfit, which has managed just one league win in 20 attempts so far this season.
"I can only get them to do what they can do. They lost the first game of the season by five. You don't go 18 games of the season without winning if you're that good, do you?" Redknapp asked. "Mark Hughes is not a bad manager, he's not an idiot. When it comes to actually what you've got here, you look at the situation, you realize that you don't go that long without winning a game. There's got to be a problem somewhere. You haven't got a magic wand. You're not going to come in and go: 'Ok lads, you lost the first 14 games, I'm going to do this and we'll start winning'.
"We've been in every game. Today was the first one we haven't been in the game. We drew the first three, then we won, then we got beaten by the odd goal twice. The late goal at Newcastle, we deserved something out of West Brom… Today, I'm afraid, their team was on a different level in all honesty."
The former Tottenham boss went on to hint at unrest in the dressing room and underlined the importance of unity.
"I know what the problems are, but I don't want to say publicly it's one or two," he said. "You have to have everyone together as a team if you want to get out of trouble. You only need one or two who don't buy into that and you have a problem."