Despite dominating the first period, Inter conceded a second-half goal through Portuguese winger Francisco Conceicao, who brought the Allianz stadium to its feet after 74 minutes following some clever footwork from Randal Kolo Muani.
"There is a lot of regret and disappointment, but the boys showed great organisation and courage," Inzaghi told DAZN.
"We needed to score more goals and finish the first half with a lead," he added, pointing to Inter's recent away defeats, including a 3-0 loss at Fiorentina, to underline the need for improvement.
The coach explained that his decision to make three substitutions in the 62nd minute was due to Juve's superiority after the break and Inter's lack of fluency.
"We had to do better, the last situation was wrong. In the nine years I've been in Turin, I've never had so many chances. It hurts to lose, we really wanted to win. Everything is still open, but we need to change the tempo," added Inzaghi.
Inter could have finally moved ahead in the title race after Napoli were held to a 2-2 draw at Lazio on Saturday but now sit two points off the pace with 54 from 25 games.
Inter visit Antonio Conte's Napoli side on March 2.
"It will be an important game, like tonight, but we have other games first," added Inzaghi, whose side host Genoa on Saturday and Lazio in the Coppa Italia quarter-finals on Tuesday. "We need to do better than we did tonight," he added.
--Reuters--