Van Gaal made some critical comments in an interview last week in which he claimed only United's results have improved, rather than the style of play, when Solskjaer's team are compared with the group he inherited from Jose Mourinho.
It was an observation that seemed to be borne out as United laboured to an uninspiring 2-1 win over Watford on Saturday, Solskjaer's 15th victory in 20 games in charge.
But it was also a result that keeps United firmly in contention for a top-four finish, a prospect that looked nearly impossible when Solskjaer took over as caretaker for the sacked Mourinho in December.
And, as he prepared to take United back to the scene of their FA Cup quarter-final defeat to Wolves, Solskjaer was happy to launch an impassioned defence of his team's style of football.
"Louis is entitled to his opinion," he said. "Some games we've pressed really high, won the ball up there and dominated. He is probably talking more about the PSG game, which was a game that we had to defend really well in the circumstances and counter attack. It's about where you win the ball. You want to defend to win the ball to go forward. You have to win the ball to then attack.”
He continued by explaining: "If you can attack quickly as we did today, then why not? As long as when you win the ball, your intention is to attack. The foundation in any team is to play well without the ball. If you can do that, then you've got a great chance. I'm very happy and grateful that I have inherited a team that has had a great education.
"Most of the players here have had Mourinho, van Gaal, Moyes and Fergie. They know both sides of the game.
"Of course we will have to add one or two, but they know what I will demand and expect from them."
Since Solskjaer took over the reins at Old Trafford, no team — not even runaway leaders Manchester City or Liverpool — has amassed more league points than United, although a top-four finish is still far from certain.
Klopp hails Liverpool's will after dramatic win
Liverpool's willpower is keeping their Premier League title hopes alive, admitted manager Jurgen Klopp after his side moved back top of the table in dramatic fashion with a 2-1 win over Tottenham at Anfield on Sunday.
"I told the boys after the game there are 500,000 ways probably to win a football game. Today it was rather ugly, but without a bit of luck you cannot be in the position we are," said Klopp. "If we are top of the table after the last matchday it would be a championship of will."
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