Carlos Tevez's brace looked to have the Serie A leaders heading for a comfortable victory at the Stadio Marc'Antonio Bentegodi.
But second-half headers from Luca Toni and Juanito Gomez Taleb saw Verona pinch a point, with the equaliser coming in the 94th minute.
Mandorlini was thrilled with his side's fightback, with Verona sitting sixth and equal on points with fifth-placed Inter.
"Today, we faced off against the best team in the league that had put us under pressure from the very first minute," he told Mediaset.
"During the half-time break, we all looked at each other and realised that we needed to change things to get back into the game.
"And eventually, we were rewarded with a positive result. Against Roma and Napoli we weren't able to play our game but today we were able to do so and I'm happy with the outcome."
Mandorlini felt his team were unfortunate with some refereeing decisions but was more focused on the result.
"We were unlucky in some instances. There were some errors but what matters is the final result and right now we're not thinking about anything else," he said.
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