Cabaye struck twice as the Magpies ended a four-match losing run with a 3-1 victory at Upton Park that forced injury-hit West Ham back into the relegation zone.
Newcastle are positioned eighth in the table, seven points adrift of fourth, and Cabaye refuses to rule out a challenge for Champions League qualification.
"We are in good shape. The Champions League is a bigger level, but we have the capacity to just stay next to the big teams," Cabaye said.
"If we are still in a similar position to challenge for the top four by the end why not?
"We can work without pressure for the moment and it's good for us.
"Now we just have to focus on the next game and we will see what is going to happen for maybe the last four or five games where we are going to be.
"If we can fight for something, why not? But we are just confident and thinking about the next game."
Cabaye, a transfer target for Manchester United and Arsenal, was the outstanding player on the pitch at Upton Park with his all-action display rewarded with his sixth and seven goals of the season.
The 28-year-old France midfielder had been disappointed that a £10million summer move to the Emirates Stadium failed to materialise with Newcastle manager Alan Pardew admitting his head had been turned.
But although his strong form continues to make him an appealing option for United and Arsenal, it has also won over the supporters and management at St James' Park.
"For me the most important thing, as I said, is to do my best for the team," he said.
"If the manager or the staff are happy with my performance and the fans who are supporting me are happy, I am happy.
"My mentality hasn't changed, even after what happened in the summer. And I will do my best for the team every day."
Newcastle survived a second-half fightback from West Ham that faltered after Carlton Cole and Andy Carroll had missed superb chances.