This phenomenon affects fruits much worse than vegetables actually. The FDA published a report that cut or peeled fruits will lose half their vitamin C content in 1-2 weeks. Over 10-25% of this loss will occur in fruits in only 5 days.
For vegetables there exists a similar, albeit less pronounced effect. When cut the flesh inside of the vegetable is exposed to oxygen and the protection provided by the peel or covering is lost.
That being said, the process of these vegetables losing nutrients is not an immediate one. Realistically the loss that occurs between you cutting the vegetables and placing them in a salad is probably distinctly minimal. I wouldn't worry too much about the nutrient loss as long as you aren't cutting the vegetables and then storing them for a long period of time.