The first real test of Jose Mourinho's second spell as Blues boss ended in a goalless stalemate, with neither side offering much in the final third.
With United taking in just their second game of the season, and Chelsea their third, there was an obvious reluctance from both teams to go chasing the game.
Lampard conceded as much afterwards, with the Chelsea midfielder aware of the need to establish momentum through unbeaten runs early on in Premier League campaigns.
He told Sky Sports: "It's tense. People talk about decider games, but it's early on in the season and neither side wants to lose. It was a bit of stalemate in those terms.
"We worked very hard to try and not let them through. The threat they have got up front, we worked hard to stop that, and they worked hard to stop us."
Chelsea skipper John Terry agreed, adding: "It was difficult. Both sides were easing off and letting us play out from the back. After that, there was a lot of pressure in midfield.
"Both midfields and attacks cancelled each other out a little bit, but neither team wanted to lose the game so early on in the season.
"It's obviously a great point for us away from home. It's a tough place to come, but it's out of the way and we move on now."
Things may have been different had a penalty been awarded after a Tom Cleverley effort struck Lampard on the hand, but the England international feels the match officials got a big call spot on.
He said: "For me, it's not a penalty. When you're challenging for a ball and you're half a yard away, what can you do?
"I was worried because in the modern day it seems to be changing, but I was pleased. I think it's common sense from the refs sometimes. I certainly couldn't do anything about it."