O'Neill's current deal expires at the end of the year, and Taylor believes the former Shamrock Rovers coach should be retained despite a record of only one win in 13 matches at the helm.
Taylor, who is working on a short-term deal as goalkeeping coach less than two years since winning his last cap, is confident that O'Neill's hard work behind the scenes will soon start to reap rewards on the pitch.
"I strongly believe the way forward is with Michael at the helm and leading us into the Euros," said Taylor ahead of Tuesday's final World Cup qualifier against Israel.
"I really feel if he carries on then everyone will be better for that continuity.
"It's going to take time, no question. Some of the young lads coming into the national side are not even playing club football, but we have a small pool of players and it's not as though we can go out and sign someone, so you do the best you can.
"Michael is very, very passionate. He's hurting as much, if not more, than anyone else.
"If you take the blip in Luxembourg out of it, the performances in all the other games - irrespective of the results - have been strong.
"It is a period of transition at the moment. It's a young squad and although the results haven't always come, the lads have set a standard of performance - getting the win against Russia, going very close to a result against Portugal.
"The lads will learn from this campaign."