Alexandre Pato hit the winner after Bernardo Corradi had cancelled out Marco Borriello's opener for Milan.
Ancelotti said: “The saving graces are the result and a few moments of the match. We struggled, Reggina were very aggressive, but we reacted well after their equaliser and deserved the win.”
It comes just three days after a crushing 4-1 victory over Lazio and gives Milan a good run-in to Sunday night’s derby against Serie A leaders Inter.
“We are slowly emerging from the difficult period with two important wins to best prepare for the derby.”
Ronaldinho was left on the bench at the Stadio Granillo and Andriy Shevchenko was a substitute, but with Borriello sidelined it’s likely one of them will face Inter.
“Both are improving. Even if they are not 100 per cent ready, they can still play. I am not worried about the derby, as in one week we have made massive steps forward. I was more worried on the eve of the game with Lazio.”