But lucky or not, defending champions France rode an Olivier Giroud winner and saw England captain Harry Kane miss a late penalty to seal a 2-1 win and book a spot in the semifinals against Morocco on Wednesday.
"It's fabulous, it was a big game," Deschamps said. "We played a superb England team who are strong technically and physically.
"It's brilliant for the players to be in the last four again. In these moments you kind of wish time could stop for a while.
"But tonight we're going to enjoy it. We got a bit lucky although we gave away two penalties. We kept our lead with our hearts and our guts."
Kane equalised with a penalty in the 54th minute to cancel out Aurelien Tchouameni's opener for France, but the Tottenham Hotspur star missed a second penalty half an hour later, sailing his attempt over the bar.
Giroud, who passed Thierry Henry to become France's all-time top goal scorer earlier in the tournament, said Les Bleus had to be at their best to beat England.
"This goal tonight, the 53rd, is even better [than equalling Henry]. Just before I had a chance that I should have hit harder and scored," Giroud said. "I thought I might get another chance, and when it came to me it was an unbelievable feeling to score.
"You need to keep believing. [Antoine Griezmann] gave me a super ball, it's so good for the team, it's awesome.
"We knew the potential of this young England team. They have everything, but we played a solid game, we tried to hurt them on the break. We went for it with all our mental strength."
France, who became the first defending champion to reach the semifinals again in 60 years, will be heavy favourites on Wednesday. After beating England, Deschamps revealed his admiration for Morocco -- the first African team to reach the semis following their 1-0 win over Portugal earlier in the day.
"We will prepare for the next game thoroughly. Morocco deserve praise," Deschamps said. "Maybe they were not expected here [in the last four], but they conceded only one goal and then, seeing them here is not a surprise at all."
Information from Reuters was used in this report.