The former Manchester City man started in the goalless draw against Arsenal despite being put on the transfer list by the Magpies following comments made about the club’s policy on his Twitter page.
And the outspoken midfielder was involved in a fracas that saw Gunners forward Gervinho given his marching orders.
But Taylor thinks Barton was Newcastle's star man in their opening game and wants him to stay at the Tyneside club.
He told ESPN, when asked about Barton’s future: “I hope so, he played fantastic today for us. He’s a big player for us as well. He was absolutely outstanding today.”
On the Gervinho incident Taylor added: “It’s not for me to comment. It’s as simple as that. The referee made his decision and at the end of the day that’s what he did. So I can’t say anything for that. I didn’t see a thing.
“The first half was really difficult. They had a lot of possession but we came back in the second half and gave them a good game in the end.”
Team-mate Jonas Gutierrez added: “They are a really good team, they didn’t have a few players that are really important to them but I think this was a really hard game, a level game and a draw [was fair].
“It’s the start of the season so we have to take care of what say about the team or the club. This is the first game; it is a good result for us. But now we have to push on.”