Injury-hit Milan opened the scoring in the ninth minute when Robinho pounced on a defensive error to hold off Gerard Pique and beat Victor Valdes in the visitors' goal after a nice one-two with compatriot Kaka.
Lionel Messi levelled in the 23rd minute but despite being a thorn in the side of the Milan defence throughout, the Rossoneri weathered the storm at a packed San Siro to secure a precious share of the spoils.
Having spent the past month looking nervously at his casualty list, Allegri welcomed the result against a Barcelona side that won the title in 2011 and has made it to the past two semi-finals.
"I'm happy with our overall performance. Mistakes are part of the game and conceding a goal against Barcelona is always to be expected," said Allegri.
But he had a special mention for Kaka, who returned from a month-long injury lay-off in a 1-0 league win over Udinese on Saturday to produce a display which Allegri says should serve as an example.
"Kaka tonight showed the champion he is, not just in terms of his technical ability," added Allegri.
"He played an intelligent game. He was an example for the rest of the side.
"But I want to offer my compliments to the entire team. We had to be extra focused tonight, against a team like Barcelona you have to have eyes all over the pitch to keep track."
At the halfway stage Milan remain second in Group H on five points with a two-point deficit to Barca, but with Celtic now just two points adrift after the Scottish champions' 2-0 win at home to Ajax.
Milan next face Barcelona away on November 6, visit Celtic nearly three weeks later and wrap up their bid for a place in the last 16 knockout phase by hosting Ajax on December 11.
On paper, the Italians appear to hold the edge over Celtic, who have yet to visit Ajax, host Milan and then visit Barcelona having succumbed to a 1-0 defeat at home to the Spanish giants.
Allegri, however, refuses to believe the runner-up place that offers a place in the last 16 is guaranteed.
"We've still got Barca and Celtic away from home and Ajax at home, so we have to take things game by game. All of those games will be crucial for our qualification chances," he added.
Robinho missed a golden chance to put Milan ahead when he bizarrely let the ball go past his legs following a cross from Kevin Constant as the Brazilian ran down on goal.
However Barcelona ultimately dominated the second half and their failure to secure the win that would have virtually secured their place in the last 16 was largely down to Milan's astute defence.
Coach Gerardo Martino said: "It's a good point for us."
But the Spaniard was visibly frustrated. "If you look over the 90 minutes I think we deserved to take more from the game," he added.
Allegri now hopes Kaka, who moved to Milan on a free transfer from Barcelona's arch rivals Real Madrid, can be as inspirational at the Nou Camp.
"We all know how much Kaka can contribute to this side," added the Italian.
"This is a really precious point for us. Now we will go to the Nou Camp looking to play and hope we can take something from the game."