O'Neill's tenure has yielded just one win from 13 matches.
"I strongly believe the way forward is with Michael at the helm and leading us into the Euros," commented Taylor.
"I really feel if he carries on then everyone will be better for that continuity. It's going to take time."
Taylor, who is working on a short-term deal as goalkeeping coach less than two years since winning his last cap, believes O'Neill needs to stay on when his contract expires at the end of the year.
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Defeats in Luxembourg and Azerbaijan in the last two World Cup qualifiers have proved particularly frustrating for the former Shamrock Rovers boss and his coaching staff.
But there is more to the story, with O'Neill working hard behind the scenes to strengthen the Northern Ireland set-up from the bottom, while also overseeing a changing of the guard in the senior side.
Talks with IFA officials will resume after Tuesday's final qualification match in Israel, and Taylor hopes they go well.
"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.
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"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 and going very close to a result against Portugal at home. The lads will learn from this campaign."
If O'Neill does get the chance to continue his work with Northern Ireland, it is highly likely he would ask Taylor to remain part of his backroom staff.
At 42, the former Fulham and Birmingham goalkeeper is only just starting to get used to the idea of his playing days being over, but he would be keen to remain involved at club level even if he was offered a full-time role by the IFA.
"I sat down with Michael and he asked me to help out for five games. If he stays that doesn't necessarily mean I stay on, we'll have to sit down and talk.
"I had hoped to play again this season but I've had a niggle with my shoulder and it's set me back a bit.
"The coaching is something I'm very keen to progress with and there's no reason why I couldn't combine Northern Ireland coaching with a job at a club."
Northern Ireland goalkeeping coach Maik Taylor has called on the Irish Football Association to hand manager Michael O'Neill a new contract despite the side's disappointing run of results.