After returning to Tel Aviv on Thursday, coach Eli Guttman said the Israeli delegation had been warned by security officials that they were at risk in Budapest.
"I don't know how much was known about this in Israel, the players were aware, but there were very severe warnings of a possible attack," Guttman said at Ben Gurion airport.
No major security incidents were reported during the match at the Ferenc Puskas Stadium in the Hungarian capital which ended in a 1-1 draw.
Guttman gave no give further details. Hungarian police said the Israeli team, which had their own security detail, had not been under threat but did not elaborate.
"There was no terror threat towards the Israeli soccer players," police spokeswoman Bettina Kovacs said.
Guttman said that after the match, the team's official bus left the stadium empty, as a decoy, and the players were taken to their hotel in another bus later.
"Our bus was sent out of the stadium after the match with a police escort and sirens sounding so that people would think it was us. We were asked to stay behind and we left later in a bus with the blinds drawn," Guttman said.
Israelis travelling abroad are regularly told to lower their profile and be aware of potential threats to reduce risks to their safety.
Last month a suicide bomber killed five Israeli tourists when he blew up a bus in a Bulgarian resort city on the Black Sea.
In 1972, 11 Israeli athletes, coaches and judges were killed after being taken hostage by Palestinian gunmen at the Munich Olympics.