Indeed, had Luciano Orquera converted Luke McLean's try and been successful with a penalty soon after, Italy would have found themselves 16-15 to the good midway through the second half.
As it was, Toby Flood took notched his sixth penalty of the afternoon to give England an 18-11 victory but Italy can take heart in the fact they were vastly improved from their performances in defeat in Scotland and Wales.
Brunel's side can also still finish in third place for the first time in RBS 6 Nations history, provided they defeat Ireland in Rome and France see off Scotland in Paris, and with a healthy points swing.
And Brunel revealed fitness was key to Italy's impressive second-half showing.
"The two halves were quite different. In the first half we saw England with a lot of possession," said Brunel. "We are on the right road and moving in the right direction.
"We defended well but we still had a few penalties in the first half, we had one or two good kicks and we nearly scored a try.
"The second half was quite different. Italy showed character. We showed we wanted to fight the England team. We had good possession of the ball but England had more discipline than we did and we incurred a few penalties.
"The difference was our level of freshness. We tried to train less hard in the week leading up to this match in order to have the level of freshness we saw at the end."