The Blues have made a very good start to the season, as they are in third place and only two points off top spot in the league.
While they are being lauded as contenders to win the trophy, Abraham knows they must show more consistency than last season if they want to remain in contention going into the business end of the campaign.
The Blues picked up a routine 2-0 win over Newcastle United on Saturday.
He told reporters: "I'm certainly not going to go there with that one and I think at the moment after eight or nine games it would be very easy to get excited about being in a high, lofty position.
"But we are improving ourselves. I think the first port of call this year was to close the gap to the top two Liverpool and City, who have set different levels of consistency through a season and amassing points, so we can't get carried away with ourselves at this early stage.
"We have to try to reach those levels of consistency and I'm just happy with where we're at now, so we will have to see.
"I'm not going to smile too much at the league table. It's nice to have three points when you are the first game of the weekend. But I know the league table will change.
"We can only worry about ourselves and our form has meant we're in a decent position. But consistency and doing it over a big period is the next test for us."