Goals from Harry Kane and Son Heung-min had Spurs 2-0 up inside 12 minutes at Wembley, with the South Korean then also hitting the crossbar.
Mohamed Salah pulled one back for the visitors in the 24th minute, but further goals from Kane and Dele Alli left Jurgen Klopp's men on the end of a comprehensive defeat.
Dejan Lovren endured a particularly difficult start and was taken off after 31 minutes, but Henderson feels that every Liverpool player was in danger of suffering the same fate.
"I think we didn't start well at all, so it's about being ready for the game – everybody," Henderson told BBC Sport.
"I know Dejan [Lovren] got taken off early in the game but it could've been anyone of us that came off because it wasn't good enough.
"We know there are things to improve and things to change quickly. I've got every faith that we can [improve] because we've got a fantastic team.
"But we need to work on a few things and change it quickly. I know we'll do everything we can to change it because that's the nature of us as a team.
"We've got to keep working hard. I'm sure a lot of criticism will come our way, and deservedly so. We can't keep doing it, we've got to change it quickly, otherwise you lose games and you lose them badly like we did.
"So we need a reaction quickly, we need to bounce back on the training field and in games, but like I say, I believe we can."
Klopp's side sit ninth in the Premier League and have won just once in the Premier League since August.