Adams was part of the last England side to exit a major tournament without a victory, at Euro 1988.
"It's incredibly difficult for both fans and players. I scored my best international goal against Russia in Euro 1988 (when England had already been eliminated). I remember scoring the goal, running over to our fans and them booing me," he told BBC Radio 5 live.
"They were disappointed. We'd lost the two previous games and they needed someone to blame. That wasn't a great moment for me. I was chased when I came home from the Euros.
"There were two busloads of fans who chased me in my Fiat Uno from Luton Airport. I feel for both sides of it. All the fans have paid a lot of money and the players will feel they haven't done themselves justice."
England have failed to reach the knockout rounds of a World Cup for the first time since 1958.