United equalled the Premier League's record success at Old Trafford on Tuesday, with Solskjaer's side matching their own rout of Ipswich in 1995 and Leicester's thrashing of Southampton in 2019.
The Red Devils were 4-0 up at half-time against the 10-man Saints, but refused to take their foot off the pedal as they almost doubled their goal difference in 90 crazy minutes.
"It is easy coming in at half-time and thinking we've won the game, but Harry and the gaffer especially were on to the boys, 'go out second half and do exactly the same'," James told MUTV.
"Sometimes goal difference is massive, but also for our confidence and doing the right things and this was the day we could go and do that.
"The second half takes us into the next game as well and we went and scored more goals."
Wales winger James, on as a second-half substitute, struck the record-equalling ninth goal in stoppage time to become United's seventh different goalscorer on the night.
"We are all confident at the minute, but getting the goals is great for everyone," James said after United had pulled level with neighbours City at the top of the Premier League, although Pep Guardiola's side have two games in hand.
"Everyone is involved in all the goals really, so it was nice to see and nice to go on and get my own goal as well. When people go down to 10 men it is so easy to think we have won the game already, but we had to do the right things.
"We had to do what we have been doing all week which is getting down the side, getting crosses in, which we did, and we got all the goals from there and we kept pushing the whole game to get more."
Right-back Aaron Wan-Bissaka got the United ball rolling with only his second goal following his move from Crystal Palace in June 2019 and worked well with Mason Greenwood ahead of him.
Solskjaer said: "The right side has traditionally, over the years, been a bit of a challenge for us going forward.
"We haven't found like a right-winger, right-back to fill the void when Antonio (Valencia) left but Aaron is getting better.
"I thought Mason's performance was excellent, even though he didn't score. So the two of them can form a very good right side."
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