Coventry had almost 60% of the ball on the night as Lampard’s side had 20 shots to Sunderland’s 16.
And Le Bris, who has now led Sunderland to a play-off final against Sheffield United in his first season at the club, conceded the visitors were the better team in normal time.
“It’s really fantastic because this scenario was absolutely incredible,” Le Bris told Sky Sports.
“We were probably too nervous for the first part of the game.
“During extra time, we were good. We played our football and we just enjoy it now.”
For Coventry, it’s a painful end to a season which has been on an upward trajectory since Lampard replaced Mark Robins in November.
Former Chelsea and Everton boss Lampard took over with the club 17th in the Championship and led them to a fifth-place finish, winning 16 of his 29 league games in charge.
“If anyone watched the two games, we dominated at home, we made a mistake and they scored,” Lampard told Sky Sports. “I think we dominated huge periods of this game [too]. We played, controlled and in the second half it was wave after wave.
“The players have given everything from where we’ve come from – 17th in the league in December and the players have been brilliant in the second half of the season.
“We’re not bitter, and congratulations to Sunderland, but we were the better team over the two football matches and that’s why they’ll be so happy going to Wembley.”