Mauricio Pochettino praised “fantastic” Dele Alli after the midfielder’s winner.
The Spurs boss had been concerned that his England star’s confidence had dipped after a ban from Champions League matches.
FIFA are also investigating Alli’s middle finger gesture on international duty against Slovakia earlier this month.
Pochettino has called for Alli’s critics to give him a break, and said: “Dele is a top player, one of the key players for us. It helps us, him scoring today. His performance was good, he tried and scored, that’s fantastic.”
Alli’s winner came in front of a Wembley crowd of just 23,926 – less than a third of the 90,000 capacity.
It was supplied by Kieran Trippier who had earlier set up both Juan Foyth after three minutes and Fernando Llorente 20 minutes later.
Both men, making their Tottenham debuts, missed with headers from close range.
Barnsley, playing some good stuff themselves, were not without their own chances.
Centre-back Liam Lindsay put a point-blank header wide, five minutes before the break, from midfielder Ryan Hedges’ corner.
Seconds after the restart, Barnsley striker Ike Ugbo almost caught Spurs cold.
The on-loan Chelsea teenager raced into the box, lifted the ball over Jan Vertonghen but powered his shot straight at keeper Michel Vorm.
And Alli’s finish was enough to send Spurs through. Barnsley boss Paul Heckingbottom said: “We’d have loved to have gotten something out of it, but were second best for long spells.”