"It's a tough one," said Gallagher to chelseafc.com.
"We were desperate to come here and play well and get three points. We haven't managed to do that and everyone is gutted. We need to improve and know how to win [these types of] games. There is a lot of work to be done.
"We worked hard and I thought we were playing well, battling well, but credit to them. It's a tough game when you come here. The way they play is difficult.
"I thought we dealt with that well until the first goal went in. It was a really tough game and everyone is disappointed. There is a lot of stuff we can improve on to help us win these games."
The 23-year-old took the captain's armband after Reece James was forced off with a new hamstring injury.
"It's not ideal at all," added Gallagher. "Reece is one of our best players and captain, so for him to come off is really disappointing. Hopefully, it's not too serious."