Rossi blasts 'passive' Hungary after Euro defeat to Switzerland
Rossi's side failed to live up to their pre-tournament billing as dark horses with a lacklustre display in Cologne.
They were rocked by first-half strikes from Kwadwo Duah and Michel Aebischer, who both netted their maiden international goals.
Barnabas Varga's second-half header gave Hungary hope, but Breel Embolo came off the bench to net in stoppage time in his first international appearance since 2022.
"We had a tactical misunderstanding. We didn't cope and have time to press them. The first half was very bad. We were too passive," Rossi said.
"Switzerland are very experienced, with quality players all over the pitch. Against teams at this level, you run the risk of doing bad things. They made the most of our mistakes."
Taking his share of the blame, as well as lambasting his players, Rossi said: "I'm not looking for guilty people. I'm the coach and need to take my responsibility.
"We had some shortcomings in individual performances. There aren't many strategies to stop individual mistakes.
"It's hard to say anyone did well apart from two or three performances."
Hungary's defeat leaves them three points behind title contenders Germany and second-placed Switzerland in Group A.
A loss against Germany on Wednesday would be a hammer blow to Hungary's hopes of making the last 16, and Rossi admitted he is not confident of upsetting the odds.
"We play Germany in four days. I dare anybody to bet one Hungarian forint on us. As of today that looks impossible," he said.
"Germany are a different team than the last Euros, they proved it against Scotland. In my opinion they are the biggest favourite of the European Championship."
'I like to play chess'
Switzerland have only lost one of their last 15 matches in all competitions and a win against Scotland in their next game on Wednesday would send them into the last 16.
There were 22 passes in the build-up to Duah's opener, the third-longest passing sequence leading to a goal at the Euros since 1980.
It was a welcome result for Swiss boss Murat Yakin, who had been under pressure after a rift with his players over tactical issues during the qualifying campaign.
"I trust myself. I have a strong team which is fundamental. We need mutual trust, so it is a satisfaction when we get a result like that. We can reach important goals," Yakin said.
"We have prepared for three weeks and the players have the right spirit. I have a role in creating this atmosphere.
"I like to play chess. Yesterday I had a victim who lost twice to me. I like to compare football to chess and we got our tactics right.
"We used that formation for a particular reason. We surprised Marco Rossi at the beginning maybe. You have to make the most of our qualities."
Scotland will be fighting to stay in the tournament when they face the Swiss and Yakin urged his team not to underestimate Steve Clarke's men.
"It is a completely different game next Wednesday. It will bring more confidence to our game but we have to play better against Scotland," he said.
"We have a lot to improve. The second half of the match didn't go very well. We conceded too many chances."