Boro travelled to Notts County having lost their first three matches this season but came away with three points thanks to a late winner from James Dunne.
"We've had a confidence in what we do," said Westley.
"We know that we're building. We knew we had a difficult start to the season with the number of players we've had stepping up to League One level. We've got lads who are jumping from the Conference and League Two.
"We know lads can make that jump because we've done it ourselves previously but it does take time. Not only are they making the jump but they're also getting themselves together, trying to gel and trying to understand me as a manager and what I want.
"It was never going to be an easy start despite what everyone was saying. If you're realistic you know that it was going to be a tough start. That said we've been edged out by the odd goal in three games and it was good to turn the corner with an away victory."