Cup first round and here they beat Malatyaspor 3-2 on aggregate due to the silver goal rule. However, in the second round they lost both games against Newcastle United. Rossi played in all four games. In their 2003–04 league season the team started well, winning their first 13 matches straight out. The first defeat came on matchday 24. Basel won the championship with 26 victories and seven draws, the team had suffered just three away defeats, and obtained 85 points. However in the cup they were eliminated early, in round three. As reigning Swiss champions, Basel entered 2004–05 UEFA Champions League in the third qualifying round, however, drawn against Internazionale, who won the qualifier 5–2 on aggregate. Basel subsequently dropped into the 2004–05 UEFA Cup. Beating Terek Grozny in the first round, Basel qualified for the group stage. A 1–1 draw away against Schalke 04 was followed by a home defeat against Hearts. But with two victories, 2–1 away against Ferencvárosi TC and 1–0 at home against Feyenoord, saw Basel rise to third place in the group table and advance to the knock-out stage. In the round of 32 in the 2004–05 UEFA Cup, a home game in the St. Jakob-Park on 17 February 2005, Basel played a goalless draw against Lille OSC, but the return leg were defeated 2–0 and were eliminated. Rossi played in all ten of these games, scoring one goal. Basel completed all the 2004–05 Super League season's seventeen home games undefeated, winning thirteen and drawing four. They ended the season as Swiss champions with 10 points advantage over second placed Thun. As Swiss champions, Basel entered the 2005–06 Champions League third qualifying round. However, they were drawn against German Bundesliga club Werder Bremen and they lost 4-2 on aggregate. Subsequently Basel dropped into the 2005–06 UEFA Cup, where against NK Široki Brijeg in the first round, they sealed a 6–0 aggregate win to qualify for the Group stage. Here Basel were then drawn into Group E, alongside Strasbourg, Roma, Red Star Belgrade and Tromsø. Rossi played in seven of the eight games, scoring two goals. Basel started into the 2005–06 Super League season well and despite the fact that Rossi played in all 18 games in the first half of the season, he left the club during the winter break. During his time with the club, Rossi played a total of 226 games for Basel