Man United remain a work in progress - Solskjaer after 4-0 win over Chelsea
After Chelsea twice hit the post, the Reds were lucky to lead 1-0 at half-time through Marcus Rashford's penalty.
But United improved after the break as Frank Lampard's first match as Chelsea boss ended in a day to forget.
"We know we're not anywhere near the finished article," Solskjaer said.
"We are working on improving as a team and finding a style that suits us a team. We still need time but it is coming.
"Winning is a habit. We are lucky to go in 1-0 up but in the second half our nerves settled, our confidence grew."
Solskjaer's team finished sixth in the Premier League last season, 32 points adrift of champions Manchester City and five behind Tottenham in the race for Champions League qualification.
Few outside of Old Trafford have predicted United making a title challenge this season, with many believing a top-four finish would represent satisfactory progress for the 20-time English champions.
Some supporters are not convinced United did enough in the summer transfer market, having signed three players - Leicester defender Harry Maguire, Crystal Palace right-back Aaron Wan-Bissaka and Swansea winger Daniel James - and letting striker Romelu Lukaku go to Inter Milan.
England international Maguire, now the world's most expensive defender after joining for £80m last week, was named the man of the match after a commanding display.
Wan-Bissaka, a £50m signing, also looked assured on his first competitive start, while Wales international James marked his debut with a goal seven minutes after coming on as a substitute.
"Harry has done exactly what we've signed him for, his presence in both boxes, his calmness and composure on the ball," Solskjaer, who replaced Jose Mourinho on a temporary basis in December before being given the job permanently in March, added.
"He's a leader and with him, David de Gea and Victor Lindelof they marshalled that backline really well. It is important to have strong personalities at the back.
"Aaron is so aggressive, he doesn't want to get beat, he's a proper Manchester United defender.
"Daniel made a great impact and it is the best feeling ever scoring a goal in front of the Stretford End, you cant beat that."
The performance of Paul Pogba, a somewhat divisive figure whose future was unclear over the summer, was also praised by Solskjaer after the France midfielder set up Rashford's second goal with a pinpoint long pass and also teed up James after a driving run.
"Paul can do everything a midfielder can," Solskjaer said.
"Paul can do many jobs, he can do an attacking midfield job and against Chelsea he was more of a link player.
"He's a top lad and such a professional who loves playing football. When he gets onto that pitch he grows."
Source: BBC
Source: Emmanuel Mensah
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