The Italians, who had conceded 159 points on their three previous visits to Twickenham and were smarting from an opening 39-3 hammering by France, probably had more to smile about than their opponents after making the rejuvenated English fight all the way for the points.
"After last week it was very important to have a reaction," admitted Bortalami, the Gloucester lock.
"We are not very happy because we lost and we have to look forward to keep our confidence and try to play a good game at Murrayfield. It's not very easy but we have to try to get a win up there.
"If we have the same attitude and maybe we can score two or three tries more and - possibly with a good referee - we can have a chance to win the match."
Italy coach Pierre Berbizier was angered by the sin-binning of Bortalami for a technical offence just before half-time and intends to scrutinise the match video after referee Nigel Owens awarded a series of penalties against his side which Jonny Wilkinson was quick to punish.
"We respect the referee," said Berbizier. "Our discipline was good, similar to the other teams in the tournament. But we still probably have to play something else because we are the little Italy."
England scored their only try - despite a suspicion of a forward pass - through Jason Robinson while Italy were down to 14 men and Berbizier said: "I know don't if it was a forward pass or not but everything changed with the yellow card."
Italy scrum-half Alessandro Troncon, 33, who was one of seven changes made by Berbizier following the French defeat, was named man of the match to justify his surprise recall.
"We had injuries this week and we needed experience," explained Berbizier. "He gave his experience to the team today.
"I am satisfied with the performance. We kept to our game plan all match long. We need to continue working this way."
Italy say the ankle injury suffered by winger Denis Dallan is not serious and they also hope to have Stade Francasie flanker Miro Bergamasco and Biarritz centre Andrea Masi back for the game against Scotland.