For the first time since August 2015, Juve failed to score at home in a Serie A game as they stayed third in the table.
But Allegri was pleased with what he saw from his team, saying all that was missing from their performance was a winning goal.
"Running is not the most important thing in football but it definitely helps. It allows you to bring your technical ability to the fore, and that's what wins you games," he said, via the club's website.
"We played very well – perhaps even better than I imagined. We restricted the team that's top of the league to very few chances indeed.
"Inter used up a lot of energy just trying to keep up with us and they were worn out by the end of the first half.
"There are certainly plenty of positives to take. The only thing lacking was a goal. We played well in the second half too.
"Inter have players who put in lots of crosses from out wide but we took the sting out of them by doubling up on the wings."
Allegri believes a match-winner would have been just what his team deserved against Inter.
"It's a shame we couldn't get the goal we deserved as it would have meant three points," he said.
"Winning always gives you a boost and it would have pushed us further up the table, but we're all crammed in there close together."