Klopp’s side made it five wins from as many league games at Anfield this season – their eighth in a row in all competitions – and sit three points behind leaders Tottenham.
Klopp said: “If you’re chasing a game it’s obviously a completely different task, but if you are in complete control you should stay in control.
“The last five minutes I think before half-time, all of a sudden we were a bit too deep and they just could chip the balls there and these are moments we have to improve, clearly.
“In creative situations you can always improve because the boys have a lot of potential and we have to use it fully.”
Once Liverpool broke the deadlock there was no way back for injury-hit Forest, but Klopp still remains wary of his side’s ability to protect a lead in front of their own fans.
“You might remember three or four years ago, all of a sudden we became slightly more dominant and were leading at home and always came under pressure,” he said.
“Like one-nil up meant nothing. Everybody thought ‘oh my god, 1-0, 10 minutes to go!’. Maybe they saw the equaliser coming and that’s the situation you have to grow into and the boys showed wonderful signs in all aspects.
“That’s now something we have to learn again because the key positions are obviously occupied by different players than that time, up front, midfield, last line.
“So that’s the space for improvement. Creating without losing the compactness is pretty much the idea.”
Forest’s winless league run was extended to six league games and head coach Steve Cooper admitted it had been a torrid 90 minutes.
He said: “For sure it is a tough afternoon. Coming into the game, you know you have to play really well and commit to a plan in order to get some success in the game.
“We were forced into some player selection, formation and plans through the unfortunate situation with attacking players. We had to go with a couple of players out of position.”
Cooper was without a recognised central striker after Chris Wood (hamstring) was a late withdrawal, with Taiwo Awoniyi returning to the bench after a groin injury.
“We only had one player who could play as a number nine in Anthony [Elanga],” Cooper added.
“It’s a position which is a little bit foreign to him anyway and two days ago we didn’t think he would be available because of illness.”