'We'll have to take small steps and learn to run before we can walk,' Barton was quoted as saying in Tyneside press.
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'There have been some bad, bad days. The fans have been through a lot. We're just glad to put a smile on people's faces. I'm just made up.'
Barton, 27, only played 13 times for Newcastle this season due to injury and will be out to make up for lost time in the Premier League with two years left to run on his £65,000-per-week contract.
'I haven't been here for the majority of it, but I have been watching and been in the background,' Barton said.
'I was one of the ones who was there at the start of the season, and one of the ones who wanted to stay.
'Unfortunately, I got injured and haven't been able to play as big a part as I would like.'
Barton spoke after Newcastle's 2-0 win at Plymouth on Monday night that triggered wild celebrations from travelling supporters at Home Park who were inconsolable last May following relegation.
'I've not experienced any of that before,' the former Manchester City player added. 'Winning the league and then all of the Geordie fans running on was an incredible, uplifting feeling.
'They were trying to loft me up and I said to them get me down because I don't deserve it. It is about the lads who have played all season. I've just come in and played a small part.
'It is an eight-hour bus ride and they couldn't fly so they must have had a great journey back with a few drinks. They have been magnificent all season and have been our 12th man.'