The Rossoneri put in an exemplary defensive performance to shut out Barcelona at the San Siro and grab a 2-0 win with second-half goals from Kevin-Prince Boateng and Sulley Muntari.
Allegri rejoiced in the victory but pointed out that the win would count for nothing without an equally effective display in the second leg at Camp Nou.
"We played a great game defensively," he told Uefa's official website.
"We knew that Barcelona love to keep possession, but we never lost composure. In the first half we created some interesting counterattacks but unfortunately lacked the killer pass.
"Barca made our life difficult in the first half, when they kept the ball on the flanks, but we stayed focused and now we can enjoy this beautiful night."
"The return leg will be a different game and we know it will be difficult, so it's a pity we didn't score the third at home. The boys were very good at restricting [Lionel] Messi, but we need to show the same intensity on the pitch if we want survive at Camp Nou and reach the quarter-finals."
Allegri also reminded his side of the upcoming Milan derby on Sunday with both Inter and AC Milan on level points in a fight for the third place in the Serie A table.
Milan captain Massimo Ambrosini was also realistic in not being carried away by the victory.
"We played as we had to. Maybe Barcelona played more football than us, but we didn't gave them the space to strike," he said.
"However, this is only the first half of the match, we know It's not over. Now we must to start thinking about the derby, and after that we will focus on the second leg. This victory is a real boost for us."
The second leg of the Champions League last-16 tie will take place on March 12 at Camp Nou.