The two men, who epitomise the passion of the English game, had clashed during the final at Wembley in which Arsenal won 2-0 to complete the Double.
Seconds before half-time Shearer, clearly frustrated by an opening half in which he hardly troubled David Seaman, went in late on Adams near the corner flag and was booked.
"I told Tony Adams that I was sorry after the game," Shearer said. "I found him to tell him this, but there were five or six moments like that during the game. I don't feel I made contact but wanted to make certain that everything was okay with him. I don't want to criticise the referee because they have a hard job to do."
The England captain went very close to equalising during an improved second-half Newcastle performance, but his shot came back off the post and after that Newcastle were heading for disappointment.
"I'm certain we'll not get over it for the next couple of days," Shearer said. "But I've got things to look forward to with England and I've got to put this disappointment to the back of my mind. We can't feel sorry for ourselves."
Shearer admitted that Arsenal deserved their victory although he felt that during the early part of the second half his side had hit back and given the fans something to cheer. He said: "I know exactly what they will be feeling. They deserve success and I feel very, very sorry for them and I knew they would turn up in their thousands on Sunday to welcome us home. We will be doing our best next season to turn things round and give them something to cheer."
Shearer must now concentrate on the build-up to England's World Cup campaign but the heartbreak of defeated Wembley was still etched on his face after the Magpies' defeat. He added: "Arsenal are a very fine side and they've played some terrific football this season and they deserve their success."Reuse content