The Blues were arguably the better team on the day, and even though Ole Gunnar Solskjaer's team had their moments, neither defence was breached at Stamford Bridge.
Both sets of attackers did not enjoy their most fruitful performances in the capital, and Man United legend Keane blasted the "boring" display after the final whistle.
Speaking to Sky Sports News, Keane said: "It was a poor game, I was getting more annoyed as the game went on. No desire to get in the box. Real lack of quality from United. The big games where they've not produced, that must be a concern.
"They do try and win, but these games I think their mindset is let's not be beaten. I think United are looking at teams behind them rather than trying to win matches and chase Man City down.
'I think they're concentrating on let's cement that second place. Sometimes you can have a 0-0 and have a great game, but some of these games have been really boring considering there's good attacking players on the team.
"When you're at one of the big teams the onus is on winning football matches. The first thing the managers will say in interviews is they're pleased with clean sheets, teams I played for wanted to score goals.
"We might concede one but let's try and score goals, that was more important than a clean sheet."
Solskjaer's side extended their unbeaten run in all competitions to nine matches with Sunday's draw, but they are 12 points worse off than leaders Manchester City with 12 games to go.