Note: my answer here relates to ordinary main effects rather than to simple effects, which turn out to be a terminology for the effect of one factor at a single level of the other factor.
Statistics textbooks actually say the opposite of this. In a factorial design with two or more factors, it isn't sensible to test for main effects in presence of an interaction because the main effects have no interpretable meaning in that case. In other words, you need to make sure that the interaction is nonsignificant before you go ahead and test for simple main effects.
This rule is called the Principle of Marginality and was first articulated as a general principle by John Nelder in his 1977 paper on linear models in the Journal of the Royal Statistical Society. In very simple terms, an interaction means that the effect of each factor depends on the other so, when interaction is present, there is no way to summarize the effect of any of the individual factors in isolation (which is what a simple main effect is trying to do).
Another way to think about the Principle of Marginality is that a statistical model should always include all the main effects and lower order interactions whenever a higher order interaction is included. In other words, the main effects and lower order interactions are part of the total package implied by any high order interaction.
So one needs to think hierarchically about any statistical model. Do you need all the complexity of an interaction model (with both main effects and interaction)? If yes, then no simplification is possible and you have to interpret the interactions. If no, then you can remove the interaction and start testing for the main effects. What you can't do is to make a sensible model with an interaction but missing one of the corresponding main effects --- that would contravene the marginality principle.
I don't want to be trite, but it's not misleading to think of an interaction as like a physical arch that sits on two posts. You can remove the arch while keeping the posts, but you can't remove either of the posts without removing the arch as well.
Nelder, J. A. (1977). A reformulation of linear models. Journal of the Royal Statistical Society 140 (1): 48–77.
Nelder, J. A. (2000). Functional marginality and response-surface fitting.
Journal of Applied Statistics 27 (1): 109-112. http://dx.doi.org/10.1080/02664760021862