The 26-year-old made his loan move from Aston Villa permanent last week as he became Newcastle’s first signing of the summer transfer window.
He helped The Magpies climb out of the relegation zone and up to 11th in the Premier League last season.
Last summer, Newcastle made just one permanent senior signing as Joe Willock arrived from Arsenal following a successful loan spell at St James’s Park.
But Targett is confident that he won’t be the only arrival on Tyneside this summer.
“Everyone has got that feel-good factor and I'm sure there will be a few more signings too that will be exciting,” he said. “So the hard work starts now because we really want to kick-on and get this club as high as possible.
“For me, I hope I can be part of this club playing in Europe. If we can try and get into Europe in the next few seasons that would be a massive achievement and I'm not going to give up on [becoming an] international for England so that would be a main target for sure.”
Kieran Trippier became Newcastle’s first England international since 2016 following his recent call-up to Gareth Southgate’s squad.
And Targett is keen to follow in his fellow full-back’s footsteps as he hopes to help United push towards the European places.
“The [2020-21] season, I was close [to a call-up] so I want to kick-on and improve as a player and I'm sure I can be an England international,” the left-back told NUFC TV.
“I think [European football is realistic], we've made a few good signings. You look at teams like West Ham, Wolves, Leicester, they are the clubs we want to be aiming for in these next few seasons and establish yourself as a top half team then kick-on.
“I'm really looking forward to [pre-season], it's going to be an exciting summer and I can wait for next season to start.”
The Newcastle players will return for pre-season in the first week of July with the new Premier League season set to start on the weekend of August 6. The 2022-23 season’s fixtures will be announced at 9am on Thursday, June 16.