Totti was dropped against Shakhtar Donetsk midweek, but came back to the starting XI with a double.
"He is a great player and when he is fit you can really tell. He plays when I consider it opportune and we will hold on tight to our captain," said Montella.
"David Pizarro is a special player and I realise a three-man midfield is difficult. With Claudio Ranieri he had Pizarro injured and Rodrigo Taddei wasn't covering, so the previous choices were understandable.
"When I took over the lads were lacking in confidence, but they have rediscovered it now."