Mark Hughes, who played for and managed Blackburn, saw his Stoke side match the Premier League champions for periods of Wednesday's encounter at the Britannia Stadium, but City showed their ruthless edge to record a comprehensive victory.
That halted a promising run of form for Stoke, who had gone four games without losing in all competitions.
Goalkeeper Begovic, though, is remaining upbeat and is sure 2011 finalists Stoke will not let their heads drop ahead of a tricky FA Cup tie at Ewood Park.
"They're [City] one of the best teams around at the moment and we caused them plenty of problems," he told the club's official website.
"We can take plenty of belief from that and hopefully we can bounce back pretty quickly.
"The result is difficult to take, but there are plenty of positives to take and we have to move on because we have another big game in the cup coming up.
"We have a squad filled with great character so this won't hinder us too much.
"It's a good thing that we have a game against Blackburn coming up so soon. We will analyse [the City] result and go again on Saturday."
Blackburn, who won the last of their six FA Cup triumphs in 1928, have already beaten Premier League opposition to get this far - Gary Bowyer's side winning 3-1 against Swansea City at home in round four last month.
The Lancashire club have been inconsistent in the Championship this season, though, and sit ninth, having won 11 and lost 10 of their 30 Championship fixtures.
That has left Blackburn 10 points off the top six, but they head into the match fresh from beating Rotherham United 2-1 on Tuesday.
Craig Conway scored the opener in that match and the former Cardiff City man has called on the rest of the team to contribute more goals to help strikers Rudy Gestede and Jordan Rhodes - who have combined for 23 of Rovers' 40 league goals.
"I did say I needed to score more goals before the game as it's definitely something I believe I'm capable of doing," he told Blackburn's official website.
"I also think as a midfield as a whole we need to score more goals because we cannot always rely on the strikers to do it.
"We've got a great three points against Rotherham and it sets up nicely for the cup game on Saturday."
