The 21-year-old was brought on during the first half of the Saints' 3-1 win over Burnley on Sunday, making a strong impression during his time on the field with numerous bursts down the left flank.
"It's been years and years of hard work," he is quoted as saying by The Mirror. "It's my movie moment to come on at St Mary's and make my debut.
"The thing is, it's over so quickly and by tomorrow I'll want to play again. I just want to get onto the next game and before I know it hopefully I'll be playing regularly or far into my career."
McQueen is expected to start Southampton's tricky Europa League tie against Inter Milan at San Siro on Thursday evening, with Bertrand and Targett both major doubts.