City keeper Joe Hart pulled off a superb save to deny Steven Gerrard from the home side's only real threat in the 1st half.
Liverpool then missed a host of chances before Fernando Torres outpaced Richard Dunne to give them a deserved lead in the 58th minute.
But Eriksson was impressed with how City kept fighting when we have little more than pride left to play for, with Elano going closest to levelling from a curling free-kick that clipped the outside of a post.
"I think we were in the game for the whole of the 1st half, even though Steven Gerrard had a half chance and Joe Hart pulled off an excellent save," he said.
"Liverpool then had that spell of 10-15 minutes in the 2nd half when they dominated and that's when they got the goal.
"But we came back at them and we tried everything we could until the last minute. I appreciate the efforts the players put in because they showed that they are not in holiday mode yet.
"It was good to see, it was very professional and I'm sure that they will try their best next Sunday against Middlesbrough because it would be nice to end the season with a victory.
"We had a lot of half-chances but we did not get that last pass through in the 1st half, but it was important to show our spirit."
The travelling Blues faithful showed they are fully behind Eriksson after all the speculation surrounding his future as City boss.
And although it was much appreciated by the Swedish coach, it appears unlikely to keep him in charge.
"They have been fantastic all season, and once again their support was absolutely incredible and we thank all of them," Sven added.