The Elland Road side have won only once in their last seven Premiership matches and have slipped from fourth to eighth in the table - but the former Arsenal manager remains confident.
"You always hope," Graham said. "Everyone's the same, and apart from the few teams at the top there are around 10 clubs capable of beating one another. It just depends on the day, because if it's your day you'll beat them."
The Leeds goalkeeper Nigel Martyn made a significant error for the second successive match against Southampton, failing to clear Carlton Palmer's header before it reached Egil Ostenstad, who set up David Hirst's winner.
Graham said: "It was another bad mistake and we've missed out on another three points. You can't legislate for individual mistakes. Unfortunately, the goalkeeper has made two in two games. Here's hoping he doesn't make any in the next few games. But we'll probably play a lot worse in future and win. There was some nice football played."
Carlton Palmer returned to Elland Road for the first time since his pounds 1m move last September, only to be dismissed in the 76th minute after his second bookable offence. But Graham admitted the former England midfielder had impressed him since his move to The Dell: "I think sometimes when someone moves from one club to another it's a new challenge, which is exactly what he needed."
The Southampton manager, Dave Jones, insisted Palmer's signing had been better business than importing players from abroad. "Carlton's been absolutely superb for us," he said. "When I first arrived at Southampton I made the mistake of travelling all over the world trying to find players from different countries to come and play for us. We didn't have a lot of money and I thought that with the price we're paying for them, it's better the devil you know, and the likes of Carlton and David Hirst have been superb. We're quietly getting there."
Goal: Hirst (54) 0-1.
Leeds United: Martyn; Halle, Harte, Hiden, Maybury (Matthews, 86), Molenaar, Ribeiro, Hopkin, Kewell, Wallace, Hasselbaink. Substitutes not used: Beeney (gk), Jones, Jackson, McPhail.
Southampton: Jones; Dodd, Dryden, Lundekvam (Hughes, h-t), Benali, Oakley, Beresford, Palmer, Le Tissier (Richardson, 78), Ostenstad, Hirst (Williams, 86). Substitutes not used: Moss, Todd (gk).
Bookings: Southampton: Palmer, Le Tissier. Sending off: Southampton: Palmer.
Referee: K Burge (Tonypandy).
Man of the match: Hirst.
Attendance: 28,791.Reuse content