Riyad Mahrez scored a brace, including a penalty, with Ilkay Gundogan and John Stones also on target after Fabio Carvalho had put the Cottagers in front after two minutes.
City now wait to see who we will face in the fifth round and you can find out everything you need to know about the draw below.
When is the draw?
The draw for the fifth round will be made on Sunday 6 February, before the fourth-round tie between Liverpool and Cardiff City.
That game kicks-off at 12:00 (UK) and the draw, which will be conducted by former City striker Andrew Cole, is expected to begin at approximately 11:40.
How can I follow the draw?
Supporters living in the UK will be able to watch the draw live on ITV, and it will also be streamed live on FA Cup’s official Facebook and Twitter channels.
Fans based around the world can find out how they can tune in via the FA’s list of global broadcast partners.
We will announce our fifth-round opponents as soon as the draw as made on mancity.com and the official app, and you can also find out who we’ll face on Twitter: @ManCity.
Which ball number are City?
We are ball number 15.
1. Crystal Palace
2. AFC Bournemouth or Boreham Wood
3. Huddersfield Town
4. Peterborough United
5. Cambridge United or Luton Town
6. Southampton
7. Chelsea
8. Everton
9. West Ham United
10. Middlesbrough
11. Tottenham Hotspur or Brighton & Hove Albion
12. Liverpool or Cardiff City
13. Stoke City
14. Nottingham Forest or Leicester City
15. Manchester City
16. Norwich City
When will the fifth-round ties be played?
Games are scheduled to take place in the week commencing Monday 28 February.
Round dates
Fifth Round: Wednesday 2 March 2022
Quarter-Final: Saturday 19 March 2022
Semi-Final: Saturday 16 April 2022
Final: Saturday 14 May 2022
