"He said 'look it's not gone, (but) I can feel it'. We said you've got to get off the pitch because hamstrings are notorious so we had to do that. It was good management from both."
Earlier, Dyche had said: "We're hopeful it's not a serious one. He got up pretty quick, but he was feeling it so we decided we had to make that decision."
City took a five-point lead in the English Premier League with the win and Sergio Aguero became the club's joint top goal-scorer.
The Argentina striker started the game one behind Eric Brook's record of 177 which has stood for 78 years.
After nine rounds, City has 25 points - five more than rival Manchester United which lost at Huddersfield 2-1.
Aguero, back in the starting lineup after breaking a rib in a car crash three weeks ago, converted a penalty kick in the 30th minute at Etihad Stadium.
That brought him level with Brook, who scored his goals for City from 1927-39.Aguero has made 262 appearances for City in all competitions to reach the record mark, compared to Brook's 493.
Aguero has 129 Premier League goals, third highest among active players - behind Wayne Rooney (201) and Jermain Defoe (159).Nicolas Otamendi and Leroy Sane added second-half goals for City.