Arnold was only called into the starting line-up after first-choice stopper Chris Day injured himself in the warm-up but made the most of his chance with a string of fine saves.
Boro took advantage as second-half goals by Felipe Morais and Jordan Burrow sent them through to the second round of the Capital One Cup.
Westley said: "We're lucky to have two goalkeepers of high calibre so that if you lose one the other one gets his opportunity. It's got to be like that in a winning squad - you can't allow an injury to disrupt you at any time of any game.
"You've got to be able to believe in your squad and Steve Arnold is a very able and very capable goalkeeper and an excellent deputy - he did very well.
"We're going to do a lot of learning this season and we're going to make a lot of mistakes and you can't do anything about that when you've got so many new players."
After a goalless first half, Stevenage went ahead after Oumare Tounkara was clipped by Luke Hyam just inside the box and Morais confidently dispatched the resulting penalty.
Burrow then made the tie safe when he turned in Luke Freeman's cross from close range to ensure Ipswich have been knocked out by lower-league opposition for the third season running.
Their boss Mick McCarthy said: "I thought the first half was alright, to be honest. We expected it to be a difficult game but we looked alright in the first half and then in the second half we give a penalty away that the lads are not too happy about.
"Then when I changed the team and put two lads on we had a bit of a resurgence but we gave another goal away that killed us off."