The Portuguese saw team-mate Leroy Sane have a goal wrongly ruled out for offside, which would have left the match finely poised at 3-2 to Liverpool on aggregate.
After Pep Guardiola was sent to the stands for his frustrated reaction to the poor refereeing decision, Mohamed Salah and Roberto Firmino scored two second-half goals to dump City out 5-1.
While Silva was happy with his teams efforts, he also asked for Uefa to bring in rule changes for next seasons competition.
Thank you all for the support and amazing atmosphere tonight! We gave everything we could so no regrets, he posted on Instagram.
Next year well be back to try again! Congratulations to @liverpoolfc and good luck on the semi finals. Now lets go win the premier league and end the season with a title.
Ps: @championsleague could you guys start using the VAR next season? It might be useful .
More: Liverpool FC