Switzerland took a 2-0 lead over Joachim Low’s side in Cologne on Tuesday night but goals from Werner and Havertz saw Germany draw level.
Bayern Munich’s Serge Gnabry then put the hosts ahead – Havertz providing the assist – before Switzerland scored an injury-time equaliser.
Havertz, who completed a £71m move to Chelsea over the summer, said: ‘We came back after several setbacks and showed some character.
‘We’re in the middle of a process and we’re a young side. We won’t allow ourselves to be knocked off course and we will carry on as we are.
‘We need to defend better, but there were plenty of positives on show tonight.’
Werner, who Chelsea signed from RB Leipzig in July, added on Instagram: ‘There were many good moments today! But there is still a lot of work ahead of us.’
Germany boss Low, meanwhile, said: ‘It was a very high-intensity game. Both sides took a lot of risks, but there were also several mistakes.
‘We started the game poorly, but we showed real character to come back, which was good to see. We made a number of mistakes in defence though.
‘Our plan was to play with a certain element of risk, but we need to fix those errors. We battled hard to get back into the game.
‘You can learn a lot from setbacks. We need to improve our communication and instructions.
‘This team has a lot of potential. We need to correct a few things, but then I think there’s plenty to be excited about.’
Havertz and Werner will now return to Chelsea ahead of Saturday’s Premier League clash against Southampton.