Alan Pardew led the club to sixth place in just their second season back in the top flight to secure qualification for the Europa League.
The 51-year-old manager's team face Atromitos in the second leg of their play-off match in the continental competition on Thursday, with the aggregate score at 1-1 after Taylor scored a trademark free-kick during the first match in Greece.
|13/2||Newcastle are 13/2 with Paddy Power to beat Aston Villa 2-0 on Sunday
"I have seen it all. I signed four months before we went down, so I have seen everything.
"I have seen quite a few managers in the short space of time since I have been here and it's great as it is now.
"We have got stability, we have got the fans back and we are playing good football and winning football matches, and that's the most important thing."
Taylor's prowess from set-pieces has become well-known on Tyneside, with his latest effort ensuring that Newcastle enter Thursday's match at the Sports Direct Arena on level terms.
"You practise these things quite regularly and they do tend to come off now and again and when they do come off, they are quite special," he enthused.
"They are quite special to me and the fans here love them every time they go in."
Pardew, meanwhile, was not anticipating a straightforward encounter despite Newcastle's home advantage as they seek qualification for the Europa League proper.
"They have got a couple of very good players, they have got players who can travel with the ball and that's always difficult for teams," he stated.
"The manager has got vast experience and that worries me a little bit."