The Hammers looked to be cruising to their first away success of the campaign after Frederic Piquionne and Valon Behrami put them in total command.
Cameron Jerome and Loam Ridgewell's quickfire double reply rescued a point for Alex McLeish's side.
But Jacobsen insists the Hammers have the quality to climb the table.
He said: "We just have to get out of there (the bottom three).
"When you look at the team, look at the players, the way we play, we don't belong there.
"We have to get away from that position.
"We are bottom of the league and you could sense, when they scored the first goal, a little bit of insecurity started to creep in.
"We stopped playing the football we had been playing for about 10-15 minutes and that was enough for Birmingham to score two goals and that was unfortunate.
"We have to learn from that but, having said that, we played 75 minutes of brilliant football away from home and showed we definitely don't belong in the last position in the league."
Jacobsen added: "There are a lot of positive things we can take from the game.
"When you are disappointed at getting only a point from a very difficult away fixture at Birmingham, that is a positive I think.
"We just have to build on that and make sure we get our points at home in the next two games."
Jacobsen felt the Hammers should have been awarded a penalty after he appeared to be pulled back by Birmingham substitute Jean Beausejour.
He said: "I saw it again on TV and it was definitely a penalty. It is the kind of bad luck you have when you are down there.
"It is always the same and I thought the linesman could have seen it but he said he couldn't see it and that's football.
"You can't see everything, I am disappointed but they can't see everything and, perhaps next time, they will give me the penalty."