An aspect of the performance that pleased Baines was how the Toffees nullified City's attacking threat.
The 27-year-old said: "That's the pleasing thing. The majority of the play was in front of us.
"I thought the midfield lads worked tirelessly for us and did a great job defensively. That kept them off our backs a bit.
"When they eventually did get through to us at the back Jags (Phil Jagielka) and Sylvain (Distin) stood up to them. I thought we did well."