I don't think you can do it directly via the "style" tag from HTML without referencing the Javascript classes for the panels/charts.
Instead, see the answer in this post that references the SimpleXML documentation for changing background colors.
Doc: http://docs.splunk.com/Documentation/Splunk/6.5.0/Viz/ChartConfigurationReference, see charting.BackgroundColor
@rjthibod, this should indeed be possible through CSS style as well. Panel Color, Dashboard Color etc. Please refer to Custom Layout Dark example in Splunk 6.x Dashboard Examples app.
Ideally unless we want to convert from Simple XML to HTML dashboard, it is best to use Simple XML chart configuration reference the way you have pointed out. For any HTML DOM elements which can not be styled using Simple XML Chart Configuration Reference Style override can be applied.
<html depends="$alwaysHideHTMLPanelOnlyforStyling$">
<style>
.dashboard-master{
background-color:blue !important;
}
.dashboard-row .dashboard-panel{
background-color:red !important;
}
</style>
</html>
docs link doesn't work (because of the comma) - here's one that does, for the latest version at this point in time:
http://docs.splunk.com/Documentation/Splunk/6.6.2/Viz/ChartConfigurationReference