The Blues entered Thursday’s second leg with the Swedish club having lost five of their last 10 games and Maurizio Sarri under increasing pressure.
Though the game remained scoreless at the half, Chelsea broke through in the second half to roll to a 3-0 win and 5-1 aggregate victory to advance to the round of 16.
Olivier Giroud and Ross Barkley got Chelsea’s first two goals, while Hudson-Odoi capped the scoring with an 84th minute goal – his second in the Europa League this season.
The teenager told BT Sport he was pleased with the effort and the outcome, while adding he thinks Chelsea can emerge victorious against any team remaining in the Europa League.
"I'm happy with the result,” Hudson-Odoi told BT Sport. “We all worked hard and played really well. Our mentality was strong. We paced ourselves and we deserved the win.
“The goal is a bonus for the work that the team did today.
"We are strong enough to beat any team [in this competition]."
The 18-year-old winger was making his third start in the Europa League, but still awaits the same chance in the Premier League, where he has been limited to just four substitute appearances.
Chelsea assistant Gianfranco Zola previously claimed Hudson-Odoi was liked by the coaches and challenged him to force his way past the Chelsea veterans in the line-up.
Treated to chants by the fans wishing he would stay with the club, Hudson-Odoi, even with the goal, expressed hope he had done enough to impress and play a role in the proceedings.
"Hopefully I did well and made an impact,” Hudson-Odoi said.
Hudson-Odoi has started one game in the Carabao Cup – the first leg of the semi-final against Tottenham though he did not feature in the return leg.