The Eagles romped to a 3-0 win over Spurs at Selhurst Park in the Premier League on Saturday, with the visitors being reduced to ten men just before the hour mark when Japhet Tanganga was sent off.
Following Spurs being down a man, Palace then scored through Wilfried Zaha and Odsonne Edouard (two) to run out comfortable victors.
Gallagher feels though that Spurs having a man sent off was far from the deciding factor as he insists that the Eagles were the better team even when it was eleven versus eleven.
The midfielder also claimed that Crystal Palace were hungrier than Spurs.
“It was a top performance. Even when it was eleven v eleven we were the better side. We wanted it more and had more chances”, Gallagher told the BBC.
“It was a great performance and Odsonne Edouard getting a couple of goals was amazing as well.
“I think he scored with his first touch so that will give him a lot of confidence and hopefully he can help us a lot this season.”
On a personal note, Gallagher admits that he feels he could have got on the scoresheet.
“I’m always going to give my best and try my hardest.
“I’m a bit disappointed I couldn’t get a goal because I set high standards and I felt like I could have got at least one today, but I felt like I affected the game well and helped my team and that’s the more important thing.”
Next up for Crystal Palace is a trip to take on Jurgen Klopp’s Liverpool at Anfield, a fixture followed by two home games, against Brighton and Leicester City, respectively.