The Premier League leaders were made to work hard for a point at the Stadium of Light, with Gus Poyet's men threatening the Chelsea goal on several occasions in a late flurry from the hosts.
However, Jose Mourinho's side survived to preserve their unbeaten start to the league season, something which centre-back Cahill credits to the west London club's mental strength.
He told Chelsea TV: "I think we are a different side to last year, not just personnel, but mentally I think we are different.
"They made it a scrap, but we matched that and managed to play our football as well. When teams sit back and get back in that shape, it's very tough. We saw that last year and this was no different.
"But in these sorts of games, if you don't get the breakthrough, it's important we don't lose the game, and it's a point away from home."
Chelsea will attempt to get back to winning ways when they host Tottenham on Wednesday before returning to the north-east three days later to take on Newcastle United at St James' Park, a venue where Mourinho has never tasted victory.
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