The 40-year-old Norwegian launched his reign as manager with a 2-1 FA Cup third-round victory at Newcastle on Saturday, but will now get down to the business of trying to preserve the Bluebirds' top-flight status.
Cardiff currently sit one place and a single point above the drop zone heading into Saturday's home clash with fellow strugglers West Ham, and while the manager hopes to bolster his squad during this month's transfer window, he is happy with what he has inherited.
He said: "I have a solid foundation here but it's a long season. It's the longest and hardest and most intense season in any football country, so the depth of the squad is something I am looking at, of course.
"But the quality is there. We have got loads of quality to work with and then maybe some additions to blend in.
"Of course we have not had a lot of time on the training ground, so we have had to go through a few things in the meetings.
"But the foundation is there. The performance against Arsenal, that was, for me, very pleasing to see. It was very exciting to see the way they defended against a top, top, top team, Arsenal away from home.
"They lasted 88 minutes and that was a good performance. For me, it was just to build on that a few things going forward, and we defended fantastically today."
Cardiff started brightly at St James' Park and thought they had taken the lead when skipper Mark Hudson headed home Peter Whittingham's early corner, although referee Anthony Taylor had spotted a foul and ruled it out.
Keeper David Marshall needed the help of his right post to keep out Hatem Ben Arfa's 25th-minute piledriver as the Magpies belatedly found their feet, and when the home side finally took the lead through striker Papiss Cisse 16 minutes into the second half, it did not come against the run of play.
However, Solskjaer, who knows a thing or two about how effective substitutions can be from his own playing days, shuffled his pack to great effect to drag the Welshman back into the game and then win it.
Craig Noone, who had replaced Peter Odemwingie seconds earlier, blasted a 73rd-minute equaliser past keeper Rob Elliot from the best part of 30 yards and Fraizer Campbell, who had taken over from Andreas Cornelius, powered home Whittingham's corner seven minutes later.
Solskjaer was understandably in jubilant mood as he reflected upon his first afternoon in the dug-out.
However, he was well aware that victory on Tyneside is only a start and that the hard work is still to come.
He said: "The best time you have got is when you are playing, of course. That's the best time of their lives, that's the best time of my lads' lives, they should enjoy it.
"But for me now, that time is over. You do really enjoy the moment, of course. Today was a fantastic time for us but, as I said, it was great and pleasing for the lads and we have got something to build on."