The Germans had 26 attempts on goal at the Parc des Princes on Tuesday to just two for their opponents but only Mario Gomez was able to beat inspired Northern Ireland goalkeeper Michael McGovern or the woodwork.
Germany won Group C and head to a last-16 match in Lille on Sunday against Albania, Slovakia or the third-placed team in Portugal's Group F.
There was joy for Northern Ireland too, as the Czech Republic's 2-0 defeat by Turkey meant they also advanced to the knockout stage on goal difference in their first ever Euros participation.
The Northern Irish could well have lost heavily – and with it the chance of qualification – and Mueller acknowledged Germany will need to be more clinical in future rounds.
"The goals were lacking. I alone could have drawn level in the scorers' list. We were greedy," Mueller said.
"There were improvements in our play, but of course we aren’t 100 percent happy.
"We had more chances than in the last eight games."
The Bayern Munich star combined with Gomez to create the goal on 29 minutes and he himself hit the post and the crossbar in the first half as Michael O'Neill's Northern Irish team looked in danger of being swamped.
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