Jose Mourinho's men are chasing a first Premier League title in five years.
The Blues have four draws in their last six games in all competitions, including on Sunday at home to Southampton as they missed the chance to move eight points clear.
Two of those draws were against Paris St Germain, in exiting the Champions League on away goals, while one of the two wins in the same unbeaten run secured the first silverware of the season.
"We're desperate..
not desperate, it's the wrong word - we're looking for the next convincing win, the next win, to get us back up and running," Cahill told Chelsea TV.
"We should be going out playing with freedom and not feeling the pressure.
"We should be going out and enjoying (it)
I think that comes with winning games
The next win I'm sure is just around the corner for us."
Hull, Chelsea's next opponents on Sunday, have been warned, particularly as the Blues have a full week's preparation, unusual at this time of the season.
"We're out the competitions, apart from the Premier League," Cahill said.
"We can prepare well
A week, which is rare for us, to prepare for the next game, which is important."
Chelsea lost on New Year's Day at Tottenham - whom they beat two months later in the Capital One Cup final at Wembley - but since exiting the FA Cup to Bradford, have won half of their games in an unbeaten 10-match run.
The Blues' nearest rivals Manchester City lost at Burnley on Saturday but Mourinho's men were unable to fully exploit the slip, instead enhancing their advantage, which includes a game in hand, to six points.
Mourinho refuses to believe it is purely a two-team race between Chelsea and City, with Arsenal seven points behind and Manchester United eight adrift.
The draw with Southampton came in the first match after the European exit to PSG.
Cahill, who has won the European Cup with Chelsea, but is yet to win a Premier League title, said: "Playing for this club the expectations are so high
We didn't lose the (PSG) game, we drew
All of a sudden everyone's saying 'what's happening here?'
"As players we have to focus on the job in hand and that's the Premier League.
"I'm sure we'll kick on
Man City dropped points and we picked up another point
Our goal difference is good.
"It's by far the end of the world, but we're looking for the next result.
"It's a massive opportunity for us this season, everybody knows (that).
"Ten games left to go now and we're in a fantastic position."
Mourinho bemoaned Southampton being awarded a penalty and Chelsea being denied one when Branislav Ivanovic appeared to be tripped by Dusan Tadic.
Ivanovic said on chelseafc.com: "I was at full speed, he stood on me and I went down
The decision was the referee's (Mike Dean), so I don't have anything to say."
Southampton withstood a late onslaught from Chelsea, with Fraser Forster performing well in goal.
The former Celtic goalkeeper told Saints' YouTube channel: "We've got a fantastic belief as a team.
"We keep moving forward and we can do that
On any given day we can match teams.
"It's just about trying to do that consistently.
"We're going to keep working as hard as we can right until the end."
Ronald Koeman's men are sixth, one point behind fifth-placed Liverpool, ahead of next week's match at home to Burnley.
"We can be very proud of what we've done," Forster added.
"But it's only a good point if we go into next week's game, work as hard as we can and come out of that with a result as well.
"It's an important game, a tough game so it's vital we get another good week of training and then see what we can do next weekend."
Source : PA
Source: PA