Cahill admits they are going into the FA Cup fourth round tie at Brentford on Sunday struggling for confidence but is adamant they don't lack desire.
He told the London Evening Standard: "I would hate to think players have lost their hunger after winning the Champions League and I don't think that's the case. We would be really struggling if that was the situation.
"The hunger is still there, it's just not happened for us. We have come so close on many occasions and not quite got over the line.
"We can't let this season slide away. I wouldn't say we have thrown trophies away but we have missed out on a lot of opportunities.
"We had seven to go for and we have let a few slip away which is disappointing but we have to keep going. There is still a long way to go until the end of the season and we have to make sure we finish where we want to so we can be in the Champions League next year.
"We also have to go all out to win the FA Cup and keep hold of the trophy we won last season.
"The team made a lot of changes in the summer and there are a lot of young players in there now.
"It takes time but at a club like Chelsea you don't want to be letting trophies pass you by."