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Striker Jamie Vardy's penalty in the 15th minute proved the difference in the contest as Leicester claimed their third win in seven days following Monday's 4-1 victory over Leeds United and a 4-0 Europa League thumping of Braga on Thursday.
"I think it's the best win of the three this week. With so many players out and such a tough schedule, it was an incredible performance. We had to show a different side to the team today," Rodgers told Sky Sports.
"If you think of the games we've had, we know sometimes we have to show that (resilience). You're not always going to have it all your own way. The more we work together the more we are able to deal with that pressure."
Rodgers was without defender Caglar Soyuncu (abductor) and midfielder Wilfred Ndidi (groin) among others due to injuries.
"It's important in any season your first steps are positives and with all players available it would've been really good," Rodgers added.
"But for the players we've had out for the guys to show that quality and resilience, it's what you want as a manager."
Leicester, who have 18 points from eight matches and lead second-placed Tottenham Hotspur by a point, visit Liverpool when the league returns on 21 November following the international break.