Even with Spurs facing Manchester United at Old Trafford in the next round, Coppell feels they can go all the way.
"Of course they can win it," said the Reading boss. "They are capable of winning six games to win the cup.
"You look at the players they have got and they shouldn't be where they are in the league.
"I call them part of the top five in the country in the last couple of years. It hasn't quite worked for them this year but they are a very good team."
Juande Ramos knows it is against the odds that his unbeaten run in cups will continue - he has won back-to-back UEFA Cups and the domestic knockout trophy in Spain - but is targeting more glory.
"We're going to try," said Juande Ramos. "The next game is very difficult and we know how tough it will be. They are clear favourites."
Ramos's men were ahead in the 15th minute when Keane stabbed in after Younes Kaboul's header was tipped on to the crossbar by Adam Federici.
The Spaniard said: "The most important things is to get through to the next round, we have not conceded a goal and it was quite an effort to overcome Reading.
"I'm very happy with the performance. The conditions were not good with the rain and we only had three days rest from the match against Chelsea at the weekend."
Despite victory, Ramos is concerned that cup ties will distract his side from their league revival.
"This is my biggest concern," he said.
"We are making a big effort to win in the cups and we have injured players and suspensions as a result."
Coppell picked five players from the weekend clash at Aston Villa and insisted the cup still has its magic, despite clubs going into matches under strength.
"Winning can give you a lift and help self-esteem," he said. "Who cares if you are not going to win the cup in the end? Victories in the competition against bigger teams is what the magic of the cup is."