Rafael Benitez's side conceded on the stroke of half-time for the third game in succession since their return to the Championship during their 4-1 win over Reading.
Isaac Hayden put Newcastle in front in the first half with his first goal for the club but Garath McCleary levelled things up when Ciaran Clark fouled Yann Kermorgant.
Many fans were quick to question the players' concentration levels once more following a repeat of goals conceded against Fulham and Huddersfield Town, but Gayle feels it is simply a case of players adjusting to one another in new surroundings.
"We are just a new team at the moment and we are developing together," he said.
"I am sure we are going to improve a lot and we are going to make mistakes but we will keep going and improving throughout the season.
"Hopefully we can cut them down and hopefully just keep winning."
Gayle went on to help secure the Magpies' first win of the season with a second-half brace, including a stunning free-kick, following Matt Ritchie's penalty but the summer signing from Crystal Palace made a surprising revelation about which goal he preferred.
"They were very different but if I am honest my favourite one was the tap-in," he said when discussing his two goals.
"When you see the ball like that your eyes light up and I am so thankful that the ball is played through to you.
"I would take loads of tap-ins, they are my favourites!"
NEWCASTLE 4 READING 1 (Hayden, Ritchie (P), Gayle 2)
Sels, Anita, Mbemba, Clark, Dummett, Hayden, Shelvey, Ritchie (90' Aarons), Perez (76' Lascelles), Gouffran (84' Colback), Gayle
Subs: Hanley, Janmaat, Darlow, Armstrong
NEWCASTLE 1 HUDDERSFIELD 2 (Gayle)
Sels, Janmaat (83' Armstrong), Mbemba, Lascelles, Dummett, Anita, Hayden, Shelvey, Aarons (45' Ritchie), Diame (75' Perez), Gayle
Subs: Clark, Colback, Darlow, Gamez
FULHAM 1 NEWCASTLE 0
Sels; Janmaat, Lascelles, Hanley, Dummett; Hayden (Shelvey 77), Colback (Aarons 61); Ritchie, Perez (Armstrong 70), Anita; Gayle.
Subs Mbemba, Darlow, Jesus Gamez, Sterry.
NEWCASTLE 3 VITESSE ARNHEM 2 (Leerdam (og), Gayle, Colback)
Sels; Janmaat (Sterry, 74), Hanley (Gamez, 62), Lascelles, Dummett; Hayden (Saivet, 74), Colback (Shelvey, 62); Anita (Mitrovic, 74), Perez (Armstrong, 62), Ritchie (Aarons, 62); Gayle (Gouffran, 74). Subs not: Darlow, Tiote, Thauvin.
SOUTHEND UTD 0 NEWCASTLE 2 (Anita, Gouffran)
Darlow; Janmaat (Sterry 63), Mbemba (Hanley 63), Lascelles, Dummett; Hayden (Colback 63), Shelvey (Saivet 73); Anita (Thauvin 78), Perez (Mitrovic 73), Aarons (Gouffran 63); Gayle (Armstrong 63).
Sub not used: Sels.
SPORTING LOKEREN 0 NEWCASTLE 4 (Perez 2, Perez, Janmaat, Shelvey)
Sels (Darlow 72); Sterry (Gouffran 63), Mbemba (Saivet 72), Lascelles (Dummett 63), Anita (Gamez 46); Hayden (Shelvey 46), Colback (Tiote 72); Janmaat, Perez (Mitrovic 46), Aarons (Thauvin 63), Gayle (Armstrong 63).
Subs not used: None.
DONCASTER ROVERS 2 NEWCASTLE UTD 2 (Hayden, Perez)
Sels, Janmaat (Sterry, 45), Mbemba (Saivet, 65), Lascelles (Dummett, 45), Colback (Hayden, 45), Anita (Gamez, 45), Ritchie (Gouffran, 45), Aarons (Perez, 45), Shelvey (Wijnaldum, 79), Mitrovic (Gayle, 45), Armstrong (Thauvin, 60).
BOHEMIANS 0 NEWCASTLE 6 (Ritchie, Mitrovic, Gayle, Thauvin, Aarons, Wijnaldum)
Sels, Anita, Lascelles, Mbemba, Sterry, Aarons, Colback, Gouffran, Ritchie, Saivet, Mitrovic.
Subs: Darlow, Gamez, Dummett, Wijnaldum, Shelvey, Hayden, Perez, Gayle, Janmaat, Tiote, Thauvin.