In the battle of first versus second, Carlos Tevez gave Juve the lead on the hour mark with a delightful free-kick that looked set to extend his side's lead at the top to 12 points.
That free-kick followed Vasilis Torosidis' second yellow card, but the 10 men of Roma fought back to salvage a point through Seydou Keita's late header.
Having failed to win away for the third game running, Allegri explained: "We left the pitch angry at having drawn that game. We must get back to winning ways on the road.
"We did well up until 70 minutes, not giving Roma an inch, then we stopped playing. We need to improve.
"It's a pity to leave here with a draw. We need to be better with our use of the ball.
"I'm happy with the way we played up until the 70-minute mark. We're still a long way off our target."
