Cochrane led her team-mates out for the final time on Sunday, as Becky Langley's side swept aside the Yorkshire visitors at Coach Lane.
The right-back scored a header and a penalty, following up her goal against Alnwick Town Ladies the week prior and Cochrane expressed her delight at signing off her Newcastle career in clinical fashion.
"It was incredibly special and something that will always live with me," she said. "Last weekend at St. James' Park was extremely surreal and will probably never sink in, but I never expected to end Sunday with two goals in my last appearance.
"I don't think I'll ever get over (playing at St. James' Park). It can never be changed, and to make history with such a great group of people will always trump any other footballing memory for me."
Cochrane signed for the club in 2014 and has grown into a key player during her time with the Lady Magpies.
Reflecting on her career, she said: "I think the biggest thing I've achieved for myself is the development I've had, not just as a player and leader but also as a person.
"I think football can teach people so many different lessons and if you're open to taking on the lows as well as the highs, you'll always come out stronger."
Newcastle Women were narrowly pipped to the FA Women's National League Division One North title by Liverpool Feds this season but have recorded their highest points tally (56) and goal difference (69) for over five years.
The Lady Magpies captain said: "This season has been a mixture of highs and lows with a lot of lessons, but it will be one that we will never forget.
"It'll always be the season that ran away from us, but it will also be the season that made us."
Despite no longer being able to win the league, the Lady Magpies rallied to blow Barnsley away 8-1; a performance that Cochrane believes sends a message to their rivals for next season.
"I think (the win) shows just how much potential the team has as well as how much determination they have," she said. "Although we knew we couldn't win the league, everyone went out there to show the campaign wasn't over for us.
"The professionalism from everyone was second to none."
She added her hopes for the future of Langley's side: "I'd love to see them go all the way and I do not doubt that they will. Next season I'd love to see them win the league and break every record they can. I know they're capable of it."
Cochrane plans to remain in football following her retirement, with the Newcastle United Foundation Be A Game Changer ambassador keen to inspire future generations.
"I'd like to progress with my coaching within grassroots and the player development centre," she revealed. "With the experience and knowledge I have from playing, I think I can offer a lot to the younger generation."
She issued a message to young girls who want to get involved in football: "Never let anyone tell you can't do something. If you want it enough and believe you can do it, then you'll absolutely smash it."
