The reason for this from a creative stand point could be down to the physical effects of spider-mans’ powers. So his healing factor was fighting against the effect of the gauntlet before failing or as he says in the scene he just really didn’t want to go. His instinct to stay alive was so strong that he held on just for a few more seconds.
The reason for this from a business stand point is entirely for tony stark’s reaction. No-one on team iron man other than peter actually had a relationship with tony stark so like with captain america’s reaction to Bucky dieing we get to see the horror on Tony’s face as he realizes that he put peter in that situation, separated him from his aunt and most importantly failed him as a hero. Spider-man says “i’m sorry” but tony believes he should be apologizing to peter for failing as a hero, a mentor and as a father figure injustice 2 joker costumes.
Well since Spider-Man has many powers including his spider senses, he is able to feel that something is wrong before it even happens.
In the movie, Spider-Man says the line “I don’t feel so good Mr.Stark” (Which has now become a meme) as he falls into Iron Mans arms. This is all because of his super Spidey senses as seen earlier in the movie when he is on the bus and the hair on his arm raises.
The in-universe answer, if you want it to be: Spider-Sense. Because of Peter Parker’s Spider Sense, he was aware of what was happening to him in a way no one else was, and so he had time to feel it (“I don’t feel so good”) and react to it that others did not have green arrow and black canary costumes. We’ve heard from behind the scenes that these lines were improv, so I’m sure this was not in the directors’ minds at all when filming this scene, but I think it's a perfectly good way to explain it if you’d like to have one.
And today I would like to suggest you this cosplay costume site: www.cosjj.com