The German has seen his side create a significant number of chances in their last few fixtures, but failed to convert enough to win their last two matches.
Lack of goals
Cristiano Ronaldo has come under fire for the Red Devils lack of goals this season, despite being their top scorer with 14 in all competitions.
However, though Rangnick admits the United No.7 should have a higher goal-tally, he feels it shouldn’t just fall on the 37-year-old’s shoulders.
"It’s not only about Cristiano Ronaldo,” Rangnick said in Friday’s press conference.
“He should score more goals, it’s obvious, I think we are creating enough chances and and enough opportunities in the last couple of games but we just didn’t score enough goals, but this is not only an issue with Cristiano, it’s an issue with the other players, especially the offensive players. We don’t score enough goals.
"If you bear in mind how many chances we create, and this is also something that needs to get better in the next couple of weeks. At Burnley, in 70 of those 90 minutes, it was very, very, very close to the game plan we spoke before the game and now it’s about rewarding ourselves and also getting the results we should deserve."
Harry Maguire’s form
Another player who has been in the spotlight is Harry Maguire. The United captain has been criticised by fans and pundits for his recent performances, with his positional error leading to Burnley’s equaliser on Tuesday.
However, despite this, Rangnick has supported the England international and thinks he can ‘perform’ against Southampton on Saturday.
He said: "I think he had an outstanding game versus West Ham. We could have defended transitional moments better at Burnley but the rest of our defence was not really good. We should not have allowed the counter-attack to happen.
"Harry was injured, came back, had a very good game versus West Ham and sure he can perform like that tomorrow."
This will be the 46th Premier League meeting between the Red Devils and the Saints, with their previous clash ending in a 1-1 draw at St Mary’s Stadium in August.
United will be looking to get back to winning ways in the top-flight and Rangnick is under no illusions that the club needs to beat Southampton on Saturday.
He said: "We are fully aware this will be a difficult one. Obviously, I watched the game at Spurs during the week and they really deserved to win. They tactically played at a very high level and this will be a challenge for us, but I’m sure we’ll be up for that challenge.
"We’ll prepare the game today for tomorrow’s game and we have to win the game, that’s for sure. We did well in both first-halves against Middlesbrough and Burnley, but we need top performances from the whole game against Southampton and Brighton."