"That's the one thing that disappoints me. He [Solskjaer] obviously knew they were going to sell Lukaku at some point, but not to have a centre-forward lined up seems like a mistake to me," Scholes told talkSPORT.
"Whether they did, whether it dragged on too long from the club's point of view, I don't know. They're going into a season without a centre-forward when it's a club that is known for its attacking style and had probably four centre-forwards in its heyday.
"So to go in there with Rashford and Martial, who you're not quite sure if they're left wingers or centre-forwards, we don't know. But I'm sure it'll get sorted."
United have scored in every match so far this season, but have only managed one apiece in their four outings since thrashing Chelsea 4-0 on the opening day.
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Paul Scholes: 'Manchester United not replacing Romelu Lukaku is a mistake'
Dimitar Berbatov has announced his retirement with a colourful statement, saying: "I will f****** miss it".
The Bulgarian striker played for Tottenham, Manchester United and Fulham in the Premier League, scoring 94 goals in 229 appearances in the English top flight.
Berbatov had been without a club since leaving Indian Super League side Kerala Blasters last year, meaning his retirement was expected.
The 38-year-old uploaded a video of his overhead kick while playing for United in a 3-2 win over Liverpool nine years ago to Instagram, before posting a longer statement.
He said: "My last game was more then one year ago, so i think its the right time now to stop and its long overdue!
"Although when i think about it, its never The End, because i will stay in the game in one way or another, the time has come to say that after almost 20 years playing football i am stooping with my professional ACTIVE football career!
"I will miss it! I will f****** miss it! Everything! The games, trainings, the goals, preparations, the pressure, my teammates... the roar of the fans when i scored another banger.
"I was blessed and work hard to have the opportunity to play with one of the best ever and against some of the best ever!
"And coming from small country this makes it even more special for me! I had my highs and of course some lows in my career, won my fair share of trophies, score some goals along the way as well! I played the way i wanna play, and i scored the goals i wanted to score!
"Thank you to all the people who helped me develop, and became the player i always wanted to be!
"Thank you to all my former teams my teammates and my coaches and staff! It was a pleasure! I know at times i was not easy to work with, but i always gave my everything for the teams i played for!"
Berbatov's most successful spell came at United, who he helped to win two Premier League titles, the FIFA Club World Cup and League Cup. His 48 goals for Bulgaria make him his country's joint all-time leading scorer alongside Hristo Bonev.
As well as his eight-year stay in England, Berbatov also played for Bayer Leverkusen, Monaco and PAOK after starting his career with CSKA Sofia. He has also worked as a pundit.