The Red Bulls opened the scoring through Jamison Olave in the 18th minute but conceded just before the break to Daniel Paladini prior to Maicon Santos scoring twice late to give the Fire their first victory of the season.
Former Everton ace Cahill, who skippered the side with Thierry Henry starting on the bench, said it was now time for the clubs more experienced players to pick up the pieces after recording just five points from their opening six outings.
"It was out of character for us, not keeping the ball. But the main thing is, it wasn't the best performance and we're going to have to look forward to next week," said the Australian.
"We learned a lesson today. Maybe we were trying to go and chase the game and win it, and in the end we got caught and they got two late goals. So, it was unfortunate but we stick together and we're going to have to go again and see what we can do next week on the road."
He added: "I think the good thing is, we have a good manager in Mike [Petke] and Robin [Fraser]. Really positive.
"The mindset is that we got a lot of good players who have played on big stages. We need to lift the lads up, all of us. We will watch the video and do better.
"What's going to make us strong is getting it together and going for it against DC United (next weekend). Because when win games and you can pick up a win away from home against DC, it changes the whole lot of this week and it can be forgotten."