Coleman came under fire following a poor start to his tenure as Wales boss but secured a morale-boosting 2-1 victory over Scotland in Cardiff before repeating the trick away from home.
|PL STARS' INTERNATIONAL GOALS
|11/2||Scotland are 11/2 with BetVictor to beat Serbia by any scoreline on Tuesday evening
"We have been low before and we have been picked back up," he told reporters. "We have got to put Friday night behind us, don't feel sorry for ourselves and hopefully get a result in Serbia.
"If you look at the last Wales game, when we played down there, both teams were getting a bit of stick.
"I don't really see much of what goes on down there but it seems to have had an effect on their team. They have beaten us twice so they are obviously on the up."
Miller acknowledged that hard work was the only route to success for Scotland given their lack of star quality compared to other nations.
"There is only one thing we can do - get our head down and work hard and get good performances and get results," he added. "There is no magic formula - it's all through hard work."