The former Manchester United striker was appointed Cardiff boss on Thursday and saw two substitutes send his new club into the fourth round.
Craig Noone made an immediate impact after coming on to equalise for Cardiff after Papiss Cisse had given Newcastle the lead before former Sunderland striker Fraizer Campbell headed the winner 10 minutes from time.
The Norwegian, who earned a "super-sub" tag during his days at Old Trafford, could hardly have been more delighted.
He said: "Of course, when you turn games around, it's fantastic. That's the best feeling you have in games, when you really deserve it, and they deserved it today because they did it themselves, the players.
"You have 90 minutes to use 14 players. I picked a team that I thought was going to give Newcastle a hard game.
"We had some knocks - I had to leave Steven (Caulker), Fraizer and Craig on the bench, to be fair, because they have had little niggles. But it worked out well.
"You want players who can make an impact."
Solskjaer insisted he never had any problem with being used in the role of impact substitute by Sir Alex Ferguson, and he threw down the same challenge to his players as that given to him by the Scot.
He said: "I was part of a team and I was part of a great team. I enjoyed doing my best whenever I got the chance, and that's the message to the players - 'Come on, make an impact. You have got half an hour to run around as much as they have done in 90'."
Newcastle looked to be heading into the fourth round when Cisse capitalised on a period of pressure by beating goalkeeper David Marshall from close range to give his side a 61st-minute lead.
However, it was Solskjaer's decision to send on Campbell and then Noone which eventually won the day as the midfielder blasted home a 73rd-minute equaliser within seconds of his arrival before the striker headed home the winner from Peter Whittingham's corner seven minutes later.
Solskjaer said: "It's not about me, though, but it's a perfect start for the new times. The lads have had a lot to deal with lately and of course, it's nice for them to start off with a win in the cup.
"It's never easy to come up here and play, especially when you go 1-0 down. There are not too many games that get turned around up here, and the lads showed great character to do that."