The Blues have been knocked out in the semi-finals of Europe's top club competition by Liverpool in two of the last three seasons, despite going into both ties as favourites.
"It has been frustrating coming so close," he told ESPN.
"The main priority for me is the Premier League. But to go one step further to the Champions League final and lift that trophy, with the players we have, I feel that it's time that we have to do that.
"If we miss out on winning the Champions League with this squad of player, it's going to be really disappointing."
Terry added: "I think sometimes it can be a mental problem - it's more mental than anything else."