Substitute Danny Welbeck had the ball in the back of the net six minutes into stoppage time.
He said: "In those big moments you need the ref to stay strong, and unfortunately he's bottled it".
"We are under no illusion that Spain were the better team for long periods", he said.
"They pressed us and we didn't keep the ball well enough".
Kane was presented with his Golden Boot for being top scorer at the World Cup amid a buoyant atmosphere before kick-off that continued with a fast start from the hosts, thanks in large part to the unfortunate Shaw.
Tesla CEO Elon Musk smokes weed with Joe Rogan on live webcast
The impetus behind Musk building and selling 20,000 flamethrowers? Musk's behavior is becoming increasingly freaky and irrational. I'm excited to see how they will develop. "We know that sustainable energy is the end point". "It's quite hard to run companies".
Shaw was making his first England start since facing Switzerland in September 2015, a week before his double leg break in a Champions League match while playing for Manchester United.
Rashford should have levelled matters in the 81st minute after combining with Harry Kane, but the England forward could only fire straight at De Gea from close range.
Shaw and Spain defender Dani Carvajal were challenging for the ball.
It was a packed 90 minutes for England's opening Nations League match, with games against Spain and Croatia - both home and away - yet to come.
De Gea had been labelled as one of the main culprits for Spain's poor showing in being knocked out by the hosts at the last 16 in Russian Federation as he made just one save in the whole competition.
"I am especially happy about De Gea's performance", said Enrique.
"The system in Spain has produced some of the best midfielders in the world". From a tactical viewpoint it's evident that England suffer against the big sides when they play Jordan Henderson as a sole defensive midfielder.