Solskjaer’s men recorded an upset 2-1 derby victory over City in the Premier League earlier this month and the teams will meet again across two legs in January.
The Norwegian said Pep Guardiola’s men, who have won back-to-back Premier League titles but are currently 14 points adrift of leaders Liverpool, were England’s best team at the moment.
“[They will be] fantastic days in Manchester. They’re the best team in England and we’re confident going into the semi-final,” Solskjaer said.
“Of course, we do really respect them and, as I said after the derby last time, in my opinion, they are the best team in England.
“They can out-football you so we need to get our game heads on and be ready for them again.
“But we’ve shown them that we can cause them problems. I think they will be two fantastic games.”
The Red Devils laboured through the first half of their match with Colchester, and despite their large possession advantage, the scoreline was deadlocked without a goal at the first break.
But the floodgates opened early in the second-half with three goals in 10 minutes as Rashford exploited space given to him by Colchester’s right-back, to cut inside from the left and finish clinically in the 51st minute.
An unfortunate own goal to Ryan Jackson extended United’s lead five minutes later and Anthony Martial put the finishing touches on the match for inside the six-yard box.
Manchester City also struggled in periods against League One club Oxford United before Raheem Sterling’s brace secured a 3-1 victory on the road.
Joao Cancelo had put City in the lead mid-way through the first half but Matt Taylor forced a shock equaliser shortly after the second half restart.
Leicester City and Aston Villa were drawn into the Carabao Cup’s other semi-final, after the Foxes outlasted Everton penalties following a 2-2 draw at the end of 90 minutes.