Having conceded a first-innings deficit of 215, the tourists dismissed Australia for a second-innings 138 to leave a victory target of 354.
England closed day four on 176 -4, needing another 178 runs to level the five-match series, with skipper Joe Root unbeaten on 67.
The late dismissal of Dawid Malan took the shine off a fine day for England, but Anderson believes his side are content with their efforts.
“It could be a lot better for us,” said Anderson. “Three down would be amazing. Losing Dawid at the end there was tough.
“But we would take this position from the first innings. Bowling poorly first innings and batting poorly first innings, we would have taken this position.”
England silenced their critics with the bat, showing more application and fight to keep the Aussies at bay, with Root and Malan leading by example.
“There is no doubt in that dressing room. We know we can fight and have a lot of determination,” added Anderson.
“The first two innings in this game we were really frustrated. There was a bit of anger as well as we didn’t do ourselves justice.
“But we have come out with the ball and now with the bat. We have done ourselves proud so far and hopefully we can do the same tomorrow.”
England did not hit their usual high standards with the ball after winning the toss on day one.
But they learned their lesson second time round as Anderson took his first five-wicket haul in Australia to skittle the hosts.
“We are very happy,” the Lancastrian added. “We did a lot of good stuff last night with the ball swinging around under the lights.
“We didn’t think it would do as much today, it didn’t, but we just tried to pitch the ball up and cause them as many problems as possible.
“We knew they would be aggressive at times and try to set up a big score and a declaration, but we wanted to bowl them out.
“I thought all the bowlers did fantastically well.”