Reds captain Jordan Henderson is likely to be sidelined for another couple of weeks, with Keita and Oxlade-Chamberlain vying for his position.
Oxlade-Chamberlain made an immediate impact having replaced Keita against West Ham, playing a pivotal role in turning a 2-1 deficit into a 3-1 victory.
The pair are again contesting a starting berth against Watford on Saturday but Klopp did not want them to think they had to outdo each other.
“They’re not competing against each other and hopefully they don’t see it like this. It’s not like this,” he said.
“They offer naturally different things. Naby can play better, obviously, and has played better. But that wasn’t the reason the (West Ham) game was like it was.
“Then Oxlade came on, really fresh and with his natural skill, having direction, speed, it’s a different player.
“In different situations we need different players and they all are exceptional.
“Until the change, we were more fixed in positions. It wasn’t flexible enough or unpredictable enough, we were too easy to defend, we didn’t really come through.
“In other situations we were too high on the wings and were hit on counter-attacks.”
Liverpool’s game against West Ham was the first time they had been behind in a Premier League match since November 2 at Aston Villa.
“I watched the game back, and in that game being 2-1 down helped us a little bit because the direction after that, a lot of things were different,” added Klopp.
“I didn’t know it was the first time since Villa, but the boys reacted well and that’s the only thing we have to know.
“Some people used the word complacency, that they saw glimpses of that. I didn’t see that at all.
“It’s a long season and the concentration level can drop from time to time in all teams, in games and between games. How much the boys fight for a result is exceptional.
“There is no fear about anything, but we also don’t take it for granted that there will just be one or two goals up.
“This game (against Watford) will be tough. I said it, 100 per cent. I don’t want people to think we are going to win 6-0. It just will not happen.”