Jamie Slabber scored the all-important goal with a precise header five minutes from time in a game that called for great discipline and patience from the boys.
The team were never allowed to strike the rhythm they achieved in the superb win over Portsmouth in round three, but showed good character and perseverance as Swindon sought to frustrate and break up play.
"I think they saw us at Portsmouth and did quite well," said Pat afterwards. "They closed it up, made it really tight in midfield and made it difficult to get the ball to young Mark Yeates, who is really our springboard.
"There were two factors at play - they frustrated us and the evening got to one or two of the kids. It wasn't anywhere near the level of performance we saw at Portmouth.
"It really needed an experienced head out there to help them and, of course, we haven't got an experienced head. It's up to the kids."
Playing on the White Hart Lane stage was a new experience for most of the boys and Pat explained that it is a platform on which they must excel if they are to progress at the club.
"It is a terrific experience for them and we were saying afterwards that they've got to learn to cope if they want to be Spurs players - playing at the stadium with people watching.
"They got the result and now we go to Crystal Palace or Notts County. We'll have a good look at them when they play in the next couple of weeks.
"It moves the season on for us like it did last year and, if we get a result against Charlton on Saturday, we're back in the push for the under-19s section."
Pat Holland conceded that a stubborn Swindon Town had done their homework after our under-18 side left it late in the FA Youth Cup fourth round tie at the Lane on Wednesday evening.