Solskjaer got off to the perfect start as Manchester United boss as his side beat Cardiff 5-1.
Marcus Rashford, Ander Herrera Anthony Martial and Jesse Lingard were all on the scoresheet for United as they played with attacking verve and swagger.
United are now eight points behind Chelsea and Arsenal, who are level on points in fourth and fifth.
And Solskjaer says United have closed big gaps before and can do it again.
Solskjaer said: ”We take one game at a time now.
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“We’ve caught up eight or nine points before but we’ve got to go one step at a time.
“I was proud and humble at the reception from the fans, it has been an emotional all week.
“But it’s a start and we move on.”
Solskjaer then expressed his delight at how his players had adapted under him.
He said: “We had a session yesterday about patterns of play and we wanted Ashley Young and Luke Shaw to push on more, it worked out well today.
“Your work-rate is the easiest thing to work on. It is free. It is the attitude and application of the boys.
“If we approach all the games like this – and we want them to approach them all like this – with combination play and playing the ball forward then I’ll be happy.
“The foundation was in the defending today. I thought the two centre-backs and two full-backs were brilliant today.”