The Blues progressed to the last eight of the competition after coming from behind to beat Lille 2-1 in northern France, 4-1 on aggregate, thanks to goals from Christian Pulisic and Cesar Azpilicueta.
With plenty of off-field noise given the sanctions currently imposed on owner Roman Abramovich, Alonso – who was making his 200th appearance in Chelsea blue – feels much credit should be given to the players for the way they tackled the challenge of the Ligue 1 side.
"We expected a tough game against a tough side, in a big stadium with passionate fans and that's what we got," Alonso explained post-match.
"It's the Champions League, so these are the challenges you face. We never gave up, we kept fighting until the end and we are very happy with the result and to go through to the quarter-final.
"I think both games were similar, Lille are a strong opponent. We conceded a strange goal with VAR but we never gave up, we kept fighting and we got an important win to certify that we would be in the next round.
"We performed well and deserved this victory."