Liverpool were reportedly priced out by Shakhtar Donetsk after the Ukrainian club demanded substantially more than what the Premier League side offered for the Brazilian.
The English giants reportedly put in a £38million bid for Teixeira, but Shakhtar wanted close to £50m for the 26-year-old.
And Klopp has urged Liverpool fans to stand by the club's decision not to pursue the forward.
"It’s very, very important that, yes, you can trust us," the German said.
"It was a common decision [on Teixeira]. We said, 'We can't play this game until the end'.
"We made offers, I won't say too much about that, but they were realistic, absolutely, with the premium of it being January, the Premier League, all the plusses you have when you make negotiations.
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"It’s not that we haven't got money or anything, but you have to work respectfully and responsibly. That's what we do. "We will do things, for sure. Not in this window, but we will. It is like it is and it's not you should buy and sell, buy and sell."
Klopp believes he has enough forward power with Daniel Sturridge and Divock Origi, as well as attacking midfielder Philippe Coutinho, who is set to return to first-team training this week.
"We have enough strikers, if they are all fit. So we have four strikers - although some are injured - plus Roberto [Firmino]," he said.
"If we were to find a solution in the offence that helps us not for three weeks, but three months or more, I would say OK.
"If we had, then we would’ve done it - but only for the right price, the normal price and not something else.
"The situation that we had wasn’t too easy but gave us the chance to show more faith and trust in young players than normal."