The 21-year-old playmaker joined the Railwaymen on loan at the beginning of last season, but suffered an ankle injury in a friendly against Bolton and returned to St. James' Park without making a competitive appearance for the League Two side.
But the South Shields-born youngster will be back at the Alexandra Stadium for United's first ever Checkatrade Trophy tie on Tuesday (kick-off 7.30pm BST).
And he told nufc.co.uk: "I was there on loan last season for a very short period of time so hopefully I can go there and prove a bit of a point.
"I think it was my third pre-season game when I got injured. I came back, then on my first day back training, about 20 minutes in, I did it again and by the time I came back from that the loan spell was almost finished.
"It was a bit of a nightmare but it's a great club - really good facilities, really good people, really good players - and they try to play football the right way.
"I just wish I could have made the most of it, but it is what it is."
Three points will be awarded to the winning side, with a draw after 90 minutes meaning a point apiece with an extra point going to the victors of a penalty shoot-out, using the new ABBA format.
No extra time will be played. Alongside Newcastle and Crewe in Northern Group D are Oldham Athletic and Port Vale.
"If I score, I might give it this," smiled Smith, miming an apologetic shrug goal celebration.
"When I left, I felt like the injuries were just unlucky injuries - I haven't got any sort of problem - but I think some people felt that I was injury-prone and it was my fault, when really it was just two unfortunate tackles.
"I have got a bit of a point to prove so hopefully I'll enjoy myself and it'll be a good game."
Beardsley's under-23s suffered their first Premier League 2 defeat of the season at Middlesbrough on Friday night.
United had scored eight goals in their previous two games but went down to a 1-0 defeat against Paul Stephenson's Boro.
Smith - who scored in a 4-3 win at Stoke on the opening night of the season - admitted: "I think the first half performance killed us, really. They got the goal and they could control the game from there.
"We played better second half and could have won the game comfortably. I think they were the best team we've come up against but I still think we had enough to beat them.
"It was too little too late in the end, and now we’ll look forward to the next game."
Tickets for Tuesday night's match are £10 for adults, £6 for seniors and £2 for under-16s.
