Pablo Fornals had put the hosts in front by finishing off a fine team goal, with Michail Antonio continuing his fine start to the season by thrashing an effort past Vincente Guaita.
It was not enough to keep up West Ham’s perfect start to the season, however, with Gallagher pleased with the way Palace fought back for a share of the spoils.
“To score two goals is amazing, but the team performance is the most important thing,” the on-loan Chelsea man told PalaceTV+.
“We showed great character to come back twice in this game and hopefully it gives the boys confidence.
“It definitely felt like the second-half was a lot better than the first, we knew we had to improve if we wanted to get anything out of the game and I think the boys all did that.
“We all worked hard and did what we needed to do and came out with a good result in the end.”
West Ham had seen off Newcastle and Leicester to sit top of the table heading into the third round of Premier League fixtures.
They will be hoping this was just a bump in the road as they remain unbeaten going into the September international break.
Czech Republic midfielder Thomas Soucek is happy with the seven points accrued so far but bemoaned the inability of the Hammers to make it nine from nine.
“We’re disappointed because we wanted three points,” he told the club’s official website.
“We got the draw, but I think we didn’t show our quality on the pitch like we should. Twice we were winning and we should manage the game better than we did.
“Now we have seven points from three games – it’s very good and an achievement for us, but when we had six points from the first two, we wanted to make it nine.
“We have scored 10 goals in three games, which is very good. On the other side we have conceded five goals, which is too much for us.”
“We wanted a clean sheet today, but Palace got two goals, so we need to prepare our defending for the next game. I’s still good, we’re unbeaten so it’s a good start.”
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