Redknapp told BBC Sport: "It was a big result for us, it's a difficult place to come and Southampton are a good team, but that's what you get when you all work hard. I picked 11 players to work hard and when you work hard you get your rewards.
"Remy looked sharp off the right and took his goal well. It's just a case of getting him fit. Bothroyd has not had many opportunities, I played him today and he did well."
QPR are still bottom of the Premier League following their win over the Saints.