The European Cup holders have climed the table in recent weeks, winning their last six league games without conceding a goal and the significant improvement has pleased the captain.
Gerrard said: "We feel as though we're significantly improving in all departments.
"We're getting consistently good results against the top sides, and I think we're emerging as challengers to Chelsea.
"We did it in Europe last year, and our intention has always been to do the same in the league. There's still a gap to reduce, but I don't think anyone can say we've only done it in the big games now. We're producing it week in, week out and we know that's got to continue.
"In seven, or eight matches against Chelsea there's been very little between the sides. Our problem has been showing that against other sides, but we're a lot better now.
"The manager has gone on record saying he intends strengthening in January and that's going to make a difference too.
"There have been times recently when we had a good opportunity to make the final step up and we haven't really taken it, but now everyone's a lot more confident it's going to happen.
"Tuesday night was important for us psychologically. There was a lot of talk before the game about the result not mattering, but the way we performed showed that wasn't how we felt at all.
"It's fair to say there was a lot of bluffing going on before the game, and the fact both managers picked strong sides showed how they really felt.
"We're on an excellent run and we didn't want to let it slip against Chelsea.
"We'll take a lot from the fact they couldn't break us down, and with just a bit more quality with the final ball in the second half we could have beaten them.
"You never know how the draw is going to work out, but I think it's a big advantage winning the group.
"We know it's going to be tough no matter who we play, but there is a lot more chance of playing the best sides in Europe when you finish second."
