Jose Mourinho's Blues came to Old Trafford on top of the league and will depart Manchester in the same position after giving away little to the reigning champions who played their first Premier League match under David Moyes at home.
After the contest, Terry said it was a very satisfying point even though the game never reached the heights it could have.
"Neither of us had too many chances to win the game," he told Sky Sports 1.
"I think both teams looked solid and it's obviously a great point for us away from home.
"It's a tough place to come. It's out of the way and we move on now.
"I think both midfields and attacks cancelled each other out a bit and neither team wanted to lose the game so early on in the season."