The Spanish heavyweights pursued the playmaker throughout the summer following Neymar's world-record £200m switch to Paris Saint-Germain.
The club tabled three offers for Coutinho, the final one being in the region of £118m, and despite the player submitting a transfer request, Liverpool rejected Barca's advances.
Discussing the failed transfer, Bartomeu told TV3: "I will not say how much we offered, but they asked for €200m (£178m).
"We weren't going to give €200m or €150m (£133m) - we decided to step away from such an expensive market, our offer was less than €100m (£88m), with add-ons it could have reached €120m (£106m).
"Money has come into football from outside the game and made [the transfer market] more expensive, which explains what happened with Coutinho."
The Brazilian made his first appearance for Liverpool this season when he came on as a substitute in the team's 2-2 draw with Sevilla in the Champions League last week.