The visitors gave the ball away while trying to play out from the back on several occasions, with Diogo Jota sparking the second-half flurry after pouncing on Nuno Tavares' loose pass.
Klopp said it was "always important to win home games" but even more so given his side had failed to win their past two Premier League outings.
A defeat by West Ham before the international break followed a 2-2 draw with Brighton at Anfield in which they had led 2-0 after 24 minutes.
"It wasn't a top-class performance but it was very controlled and mature and exciting in other parts," Klopp told Match of the Day.
"The goals we scored were well played, worked for in counter-pressing situations. I like these goals because they cause problems for the opponents - you can be greedy in these situations and we were today."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!