The 19-year-old defender captained Gers B to a 3-1 success over the League Two outfit, who brought an experienced side to the Rangers Training Centre.
The Light Blues broke the deadlock early in the first half through the in-form Findlay Curtis, before goals from Paul Nsio and Archie Stevens put the seal on the win.
Speaking to RangersTV after the victory, Webster commented: “A win is a win, and you get the three points.
“It’s good for us to beat a Clyde first-team side and good for our progression to be playing against men’s teams. We took our chances.
“It’s always helpful getting that early goal, especially as it brings a bit more calmness as a defender.
“It was a good test. We had most of the ball and there’s different challenges such as staying concentrated off the ball.
“We had to defend because of the way that they played; sitting off and playing it in-behind to their striker.
“We had to stay concentrated at all times, and it’s a good challenge in that sense.
“They have experience in the game, and they’ll give you a nudge or get their body in first going in for headers. You need to be more streetwise and prepared to deal with that.
“It’s good development for me because then I can adjust my game to what they do, and I can play my own game against them.
“I need to overcome that challenge and win my battles.”
The victory was the perfect boost ahead of next week’s SPFL Trust Trophy quarter-final clash, where the young Gers will make the short trip to Mount Florida to face Queen’s Park.
East Kilbride await the winners of the clash in the final four, and Webster believes Rangers will need to be at their best to overcome the Scottish Championship side.
He added: “It’s another cup game against a good side, just like [last night]. It’s good to get the win as it gives you a bit of confidence and we can feel good going into the game next week.
“We’re very excited for the game. It’s another good game against top opposition.
“It’ll be at a good stadium where, hopefully, the standard of football will be high and we can push through and reach a semi-final.”