The Rossoneri are in command of the last-16 tie follow's last night's victory over Blaugrana.
Allegri believes that Milan got their just rewards for hard work in preventing Barca from applying their attacking gameplan.
"The lads played well in defensive terms and didn't let them near our penalty area," the 45-year-old told Mediaset.
"We knew Barcelona kept possession for about 65% of the time, but we had five or six very favourable situations where we got the final pass wrong.
"[My players] didn't lose heart, even when Barcelona kept possession. My players all deserved this evening, as did the club and the president."
The next leg takes place at the Camp Nou in two weeks.