Eurosport - Sun, 14 Mar 12:20:00 2010
"The team are frustrated with life, with themselves. As a collective I think we are just gutted," said Johnson.
"We could have won but I am not going to say we should have won. As a team we have to find a way to win.
"It wasn't a great game to watch. There were a lot of penalties down to the interpretation at the breakdown and it kept us in our half for most of the first half.
"I thought when we had the ball in the first half we looked good but we gave it back so cheaply. We did some very good things and did some silly things. These games get tighter and tighter as the clock runs down. Ultimately it is a tale of missed chances."
Johnson still held out hopes of a positive end to the season, however, as he looked forward to the final match of the campaign against France next week.
"It is a good game for us to finish with. It is an exciting one," said Johnson.
"It will be a huge game for them and Saturday night in Paris can be difficult as Ireland have found out."
Scotland boss Andy Robinson hailed the draw with England as a "step forward" despite admitting his side had wasted another opportunity to record a first win of the campaign.
"You've got to work hard for your tries," added Robinson, who narrowly failed to become the first Englishman to lead Scotland to a Calcutta Cup victory.
"When we put England under pressure there were a couple of occasions when we chose the wrong options. We're learning and what you saw was an improvement from Italy. It will come."
The result means Scotland will finish with the wooden spoon if they fail to win in Ireland next Saturday.
"I'm really looking forward to Ireland," said Robinson. "The players took another step forward this week.
"I thought we played positive rugby, I thought we moved England around and, credit to their defence, they held up well.
"I thought we created opportunities and I thought the way we tried to play with the counter attack and some of the attacking plays we put on was very good.
"Unfortunately, again, we couldn't get over the line. But I'm really, really pleased with the way the team tried to play and played."