Szoboszlai's 96th-minute spot-kick rescued a point for Liverpool after Elanga had twice helped Newcastle United into the lead, capping an emotional afternoon at St James' Park that also saw both sets of supporters pay tribute to club great Kevin Keegan.
Szoboszlai, speaking to BBC Match of the Day, said he had blocked out the noise around the penalty decision before stepping up.
"I didn't even know what was going to be the decision or if VAR would get involved. I wasn't even there so much, I was just focusing on myself. When the decision was made, I just stepped up and tried my best.
"I decided before, yes. It's always before my run up that I decide where I'm going to go."
Reflecting on the result overall, he added: "It was a nice game. I would be more happy if we took the three points. But we take the positives, take the one point."
Asked about working under new manager Andoni Iraola, Szoboszlai said the group was still finding its feet together.
"We are still getting to know each other, the whole team and coaching staff. But we have a good company together and good team spirit and that's all that's needed to be successful."
Elanga, who scored the opener and set up Newcastle's second, admitted mixed feelings after seeing a lead slip so late on.
"Mixed emotions. It was a good performance. But disappointed to concede the way we did in the final seconds. To think the manager has been here for just three weeks and we played like that out there, it's important we take the positives from this game and apply them in the next game."
He described the emotion of scoring in front of the Newcastle crowd.
"Relief. Something I've wanted to do for a long time. I've been working hard for these moments, especially in the summer and after the World Cup. I wanted to work on my game and I took that opportunity. It was the first shot of the game. It was a moment I really wanted to take. The whole team played really well. If we can apply ourselves like that every single week, we are going to have a fantastic season."
Elanga was full of praise for Matthias Jaissle's early impact.
"Manager has been top since he has come in. The way he wants us to play, you can all see it on and off the ball. When we go, we really go for it. We could've finished off this game earlier as we created a lot of opportunities. But it's the first game. There are still 37 games left in the Premier League."
He added that the new regime had reinvigorated his own game: "It feels fun. Hopefully it looks fun for those watching. When I am on the pitch, I feel really good and that's the way I always want to feel. Thanks to the manager and his staff for instilling it in me and the rest of the team."