Germany's 8-0 rout on Friday of San Marino saw Joachim Loew's men reinforce their grip at the top of their World Cup qualifying group with a five-point lead on Northern Ireland.
Afterwards Mueller said that playing a "team of amateurs" in the "pouring rain" left Germany's stars exposed to injury.
"This is nothing to do with professional football," Mueller told German media.
"Of course, it's a highlight for San Marino to play the world champions. But these games, in such slippery conditions, leave you exposed to unnecessary risks."
That sparked an angry response from the perennial whipping boys, who are bottom of Group C with no points after shipping 17 goals in four games.
San Marino coach Pierangelo Manzaroli told Sport Mediaset: "When a small country like San Marino play against the world champions Germany, a result like this can happen.
"The important thing is we should never lose respect. People have to have self-control post-match.
"In this case, that didn?t happen.?
Alan Gasperoni, reportedly a San Marino press officer, went even further in his criticism and sent Mueller an angry Facebook rant listing 10 reasons why Germany's trip to San Marino was useful.
"Dear Thomas, you're right. There's no point in these games. To you," he wrote in comments that went viral and were widely picked up in Italian and German media.
"Moreover, dear Thomas, there's no point in you coming to San Marino for a weekend that was free of Bundesliga football when you could have been snuggled up with your wife in your luxury villa.
"Or maybe get invited to a big sponsor's event where you'd pocket thousands of euros."
His "10 reasons" included: "Your federation (and ours) pocketed money from the sale of image rights with which, in addition to paying you for your trouble, help build facilities for the children of your country, football schools and safer stadiums."
Speaking on Monday, the eve of Germany's friendly with Italy in Milan, Loew stood up for Mueller.
"In San Marino, they have a lot of very amateur players, so I didn't see anything disrespectful in the comments by Thomas Mueller," Loew told media.
"Players like him are used to playing in very competitive leagues, they're used to going up against fellow professionals," he said.
"From our point of view there was always respect for San Marino."