Eriksson's men went ahead through Rolando Bianchi's third goal in as many league games and then dug in for a point after John Carew had equalised for the home side.
City have failed to win on their travels since the opening day of the season - in sharp contrast to their form at home which has produced nine successive league victories.
Now they face vital clashes with Blackburn and Liverpool if they are to sustain their European push in the new year.
The Swede said: "If the match had finished after 15 minutes we would have deserved to win. We started well and played some good football during that time.
"Villa came at us after that and you have to expect that playing away from home - but we stood up to the challenge very well.
"I was very happy today with the spirit we showed and the right things that we did. Carew is a difficult player to handle, he's strong and has pace.
"But as long as we perform as we did today I will be happy and sooner or later we will win away from home if we go on like that."