The 2-0 victory came at a cost with Fabinho going down with an injury in the first-half.
The Reds have already lost star centre-back Virgil van Dijk due to a knee injury, which could cost him the season.
And Klopp has compared the Reds' situation to a marriage, with his team currently going through a tough period.
"It was a tough night. It's a bit like in a marriage, there are good and bad times," Klopp told the club's website.
"It's not a bad time but it's a tricky time. 100% we have to stick together and fight harder and that's what the boys did tonight. Losing Fabinho in the first half, Rhys Williams he's only 19-years old and I think he's played more Champions League games than Premier League games - that's rare. We're doing really well but its a shock for a team because now we have to sort that injury.
"We had to make the change at half time with Jordan Henderson - he said I'm fine but in these moments you have to be responsible and the plan before the game was to give him around 45 minutes so he would be okay for West Ham. It was a hard game to play. But winning 2-0 is completely fine so that's it - let's carry on."