The Rossoneri fought back twice, from 3-1 down and also 4-3, before Zlatan Ibrahimovic netted an injury-time equaliser.
"We knew that Udinese could cause us problems," Allegri said of the 4-4 draw.
"It was a good first half performance and we started well enough after the break, but gave away two goals far too cheaply.
"It's a shame, as Ignazio Abate had that chance and we could've won at the end, but the draw is the right result.
"We had several scoring opportunities and we always had the feeling we could get back into the game. We did well to believe and of course had a bit of luck too."
The only substitution proved decisive, as Antonio Cassano replaced Clarence Seedorf to provide two assists.
"Seedorf didn't play badly, but he had to come off because with four strikers and two midfielders, he was the one with the characteristics to step aside," continued Allegri.
"Simplicity is the best thing in football. Again today Cassano provided two simple and effective assists. At this moment his fitness levels mean he can only play around 20 minutes, but once he gets stronger he can start matches too."