James, a £15 million summer signing from Swansea, got a debut goal to add to two from Marcus Rashford and another from Anthony Martial as United recorded their biggest league win over Chelsea since 1965.
It was a clinical display from Solskjaer's team in the second half with three goals in 16 minutes, but James insists there is still room for improvement.
"We won 4-0, but there's obviously stuff we can work on and it's going to be a tough game next week at Wolves," James said.
"During preseason we've gone on that unbeaten run, that winning run.
"The gaffer has obviously got his style of playing; the high press and winning the ball back," James continued. "We showed that today with our counter-attacking as well.
"I think everyone was raring to go, but we can't get carried away."
"We've got a big, big test at Wolves next week and obviously they've shown how good they were, especially against us last season, so we've got to be prepared for that."
James made it a day to remember by adding his side's fourth goal just nine minutes after coming on as a substitute in his competitive debut.
It prompted an emotional celebration from the 21-year-old, who lost his father Kevin suddenly in May while his move from Swansea to United was being agreed.
"I don't think you could write it, really," James said.
"As soon as I signed here, I dreamed of something like that to happen and it did.
"I came on at 3-0, which obviously dampened [the nerves] a bit," the winger added.
"For me, it was just going out there and enjoying it, and obviously if I get an opportunity try and take them, and thankfully I did."