The manager said: "In the last couple of games we've drawn one and lost one and we've should have won both. It would be nice to put that right.
"Now we have a couple of games coming up and if we win both of them we will still be in the top six of the Premiership and in the next round of the cup. That's what we're aiming for."
The double-header at the Lane starts against Manchester City on Saturday before the second round, second leg tie against Brentford on Tuesday.
Back in the big time, City arrive in N17 with two wins from their first six games - including a win at Leeds - but Joe Royle's men could only draw against Gillingham in the Worthington Cup in midweek.
George added: "I'm a big fan of Manchester City the club because I think they've been in the doldrums too long.
"With the support and the stature of the club they deserve to be in the Premiership. So I hope they stay there - but not at our expense.
"I saw them last week against Middlesbrough live on television. In the second half especially I thought they showed a lot of team work and team spirit. They took the game to Middlesbrough and got a deserved draw at the end.
"We've started well at home and we did the same last year when we beat the top teams at home but spoilt it in the second half of the season.
"It's nice the way we've started but let's hope we can get the consistency that has been lacking in the last two away games.
"The mood around the camp is excellent, team spirit is first class and okay, we've now picked up injuries to key players like we did last season and I don't care who you are, if you lose key players for long periods it is difficult, but that gives opportunities to other players."
To listen to George's thoughts, click here
George Graham has a straight forward target for the next few days.