The Magpies got off to a bright start following Jamaal Lascelles' early header before Ivan Toney's drilled effort, 80 seconds after Newcastle broke the deadlock, and Rico Henry's volley sent the Bees into the lead shortly after the half-hour mark.
However, Joelinton equalised for the hosts with a emphatic finish in a pulsating first-half and despite trailing again in the second-half following Lascelles' unfortunate own goal, Allan Saint-Maximin secured a point for Eddie Howe's side after volleying home Ryan Fraser's cross.
Joelinton expressed his delight at netting his maiden goal of the 2021/22 campaign, his first since May, but revealed his side ought to have taken maximum points against Thomas Frank's side.
"I thought we played well," the 25-year-old forward told nufc.co.uk. "We have to try and look at what we did well but also what we didn't. We stuck together, scored three goals, and were unlucky not to get the win.
"It does feel like two points dropped. I had a great chance at the end which I should have scored. We are disappointed but we have to see what we did well, keep working hard and now focus on the next game (against Arsenal).
"We started very well, scoring the first goal but we conceded too quickly. We fought ourselves back into the game, showing great spirit and passion to play football.
"It felt really good to score. How I trained in the week (leading up to the game) seemed to show on the pitch and I'm pleased to score my first goal of the season. I will keep working hard and make sure I continue to help the team in the upcoming games."
Eddie Howe was absent for his first fixture since being appointed as Newcastle's head coach after testing positive for Covid-19 on Friday but Joelinton revealed the 43-year-old's arrival has been a welcoming addition for the squad.
Newcastle currently sit at the foot of the Premier League table, facing an away trip to Arsenal in their next fixture, but United's record signing is determined to build on the positives shown against the Bees ahead of taking on Mikel Arteta's Gunners.
"Eddie has brought in new ideas and a new style of play," the Brazilian added. "The last ten days with him have been very good, both for myself and the team. We have worked hard and we must continue that, sticking together and keep fighting.
"We stayed positive during the game and continued our way of pressing and how we wanted to score a goal.
"I thought I should've scored my chance at the end and I'm sure we would have got the three points but now I must keep working and make sure I can help the team again next Saturday."
