I have a textbox and a button inside an RadAjaxPanel. When I click the button RadAjaxLoadingPanel is displayed and button click event is fired. But now I want to display a confirmation message that button was clicked or just display any message after RadAjaxLoadingPanel stops.
It sounds like you don't know how to trigger an event when the RadAjaxLoadingPanel dissapears. There is a good example on Telerik's site here. If you scroll down to the code, you will see the RadCodeBlock with javascript functions controlling the RadAjaxLoadingPanel's behavior:
functionResponseEnd() {
//hide the loading panel and clean up the global variables
if(currentLoadingPanel != null) {
currentLoadingPanel.hide(currentUpdatedControl);
//here is where you would want to add a message or alert