"We didn't have any margin for error beforehand and now we have less margin in terms of coming fourth.
"But it depends on the other teams and how they do as well. We have to believe we can win all our remaining games and have confidence the other sides will lose.
"We just have to keep going because there are still a lot of points to play for."
Three of Liverpool's five remaining Premier League games are at home with Fulham and West Ham visiting Anfield in the next couple of weeks.
A trip to Burnley follows before the Reds welcome Chelsea for, on paper, their toughest game of the run-in, although they go to a Hull side on the final day of the season who could need a win themselves to avoid relegation.
Liverpool should have closed the gap on Manchester City to two points, but they wasted numerous chances against Birmingham.
Maxi Rodriguez hit the bar in the first-half, while Ngog missed three chances after replacing Torres.
"It was a great performance," said Benitez. "We had great chance in the first-half and in the second-half we had a lot of chances.
"It was a silly goal to concede, but the reaction of the team was good and we were attacking and creating a lot of chances. We're disappointed because it was a good performance."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.