Solskjaer's men produced a superb comeback at St James' Park on Saturday to book their place in the fourth round, Craig Noone and former Sunderland striker Fraizer Campbell securing victory with goals in the last 17 minutes after Papiss Cisse had put Newcastle in front.
And the Norwegian - who was confirmed as Malky Mackay's successor on Thursday - was quick to praise his players for the spirit shown.
"It's a perfect start to our new time," Solskjaer said.
"It's never easy to come here and play - the lads showed great character.
"It pleased me a lot the way they came back from behind. Two fantastic goals, it was something else.
"When you turn games around like we did it's fantastic. We deserved it."
Solskjaer has now already switched his focus to next Saturday's Premier League clash with West Ham, which sees the Welsh club - one point above the drop zone - host one of their rivals in the fight against relegation.
"This was a great start," he added. "But thoughts now turn immediately to next Saturday's game against West Ham."
