Pardew's place at the helm of Newcastle was under major scrutiny early in the campaign, with the club languishing bottom of the Premier League.
That prompted protests in the stands as supporters called for the former West Ham United and Southampton boss to be sacked.
However, those days seemed a distant memory on Wednesday night as Pardew's men secured a third successive win in all competitions.
This was perhaps their most impressive, with an XI missing some of Newcastle's key players overcoming a strong City side thanks to goals from Rolando Aarons and Moussa Sissoko.
Pardew told BBC Sport: "I do know what I'm doing. I think I've had most of the scalps as Newcastle manager, maybe except Arsenal and I look forward to playing them next. This was a victory for our fans.
"I've been criticised for not concentrating on the cups, but I think I've been unlucky when they've come around.
"I had a culled group and we had to protect ourselves a bit for [Saturday's Premier League game against] Liverpool. But now we can take confidence and belief into that game."
Pardew added: "It's a marvellous performance from Newcastle. Everything we wanted and tried to get from the game came off. We always carried a threat even from the first minute."
Taylor told Sky Sports: "It was a fairytale. It was a dream which all came true. It's been two years of hard graft to get back playing. What a performance that was from the lads."
