The Italy midfielder, who had just returned from knee surgery, produced a fabulous finish just before the hour to cut Inter's lead to four points over AC Milan and five over Juve.
"For morale we really needed to beat Inter because it is very difficult to stay behind this Inter side," the 23-year-old, who rose up through Juve's youth ranks, told Sky television.
"Now we have to continue on this path. We can't lose lots more points if we want to win the scudetto. However, Milan are in great form."
Most of the build-up to the big match in Turin centred around Inter's Mario Balotelli and the fact Juve fans have often chanted racist songs about the striker.
Authorities had threatened to suspend the game if there was further racist abuse but Juve fans largely behaved, even if Marchisio thought substitute Balotelli did not help himself.
"I like him but he must improve aspects of his behaviour," he said.
"Today after three incidents he threw himself to the floor. However, our fans behaved well, and I'm happy for that."
Juve's rookie coach Ciro Ferrara quickly turned his attention to Tuesday's Champions League home match with Bayern Munich, where a point will put them through to the last 16.
"We deserved the victory but now we have to think about Tuesday. There are certain games that stimulate great players. It has been great to beat the champions," he said.
Inter coach Jose Mourinho was sent to the stands during the match and did not do post-match interviews, leaving goalkeeper Julio Cesar to complain about the lack of penalties when Walter Samuel and Diego Milito went down.
"When you play a game like that you always want to win. We are still top and have a final (in the Champions League against Rubin Kazan) on Wednesday. But we also had a penalty," he said.
Inter must beat the Russian side at the San Siro to guarantee a place in the Champions League knockout round.
