Coach Luciano Spalletti tried to keep his feet on the ground after his Roma side knocked Real Madrid out of the Champions League 4-2 on aggregate after a 2-1 win at the Bernabeu on Wednesday.
"We have to be cautious and keep our heads," Spalletti told a news conference. "Too much euphoria is a dangerous thing. After all we also have to concentrate on the league and we have got a tough game coming up at the weekend.
"We have to keep our feet on the ground and take things one step at a time," added Spalletti, whose team visit Napoli in Serie A on Sunday trying to close a six-point gap on leaders Inter Milan.
Roma weathered some heavy early pressure at the start of each half in Spain on Wednesday but looked razor sharp in attack and took full advantage when Real centre-back Pepe was sent off 19 minutes from time.
Brazilian midfielder Taddei headed Roma ahead two minutes later and although Raul equalised the visitors put Real to the sword when substitute Mirko Vucinic scored with a diving header in the final minute.
"Real tried to be aggressive but my team gave nothing away," said Spalletti. "They responded to the occasion and we won because of our attitude and efforts on the night."
"I expected a tough game, but my team came here to get a result and they responded perfectly."
As to Roma's quarter-final opponents Spalletti did not want to tempt fate by asking for Manchester United, who hammered his side 8-3 on aggregate at the same stage last season.
But he said his team had learned important lessons from that defeat which had been put into effect against nine times European Cup winners Real Madrid.
"The Manchester defeat showed us a lot," he said. "Tonight we suffered at times, but we deserved to go through."
Real Madrid coach Bernd Schuster tried to remain upbeat despite the setback.
"For me this isn't a real defeat," he said. "We didn't qualify that's all. Until their first goal the game was ours but we couldn't find the net. The sending off of Pepe did us a lot of damage.
"I couldn't have asked for more from the players. They had to play with a man down. They showed great character and they kept believing they could win this game.
"The team tried to go for the win but Roma are a very tricky team to play against, harder than many people thought."