Scotland forwards Chris Martin, Johnny Russell and Ikechi Anya accepted they lost to a better team in Tuesday's in Glasgow.
The home team imposed themselves only fleetingly on a dominant England side.
"I don't think we did ourselves justice," said Derby County's Martin, who made his first Scotland start.
"On the night the better team won. We weren't able to raise our game again after Friday [the win over the Republic of Ireland], which is disappointing."
Martin, 26, was given few chances to score at Celtic Park, limited by the service to him from his team-mates and by the English pairing of Chris Smalling and Gary Cahill.
He was replaced at half-time by James Morrison.
"We need to take stock and realise the game on Friday was the main game," said Martin, in for the injured Steven Fletcher.
|Scotland winger Ikechi Anya|
|"England were a lot better than us on the night in every aspect. They deserved their win"|
"We've got to look at tonight's performance and see where we can improve.
"We have to wait a long time before we play again. There is obviously room for improvement. A performance like that puts things into perspective."
Martin was unable to bring his club form for Derby - 12 goals this season - to the international stage but he is well aware of the jump in standard.
He said: "This is a massive step up from playing in the Championship. These guys are playing in the Champions League.
"It's a big learning curve for me and hopefully I can learn from these experiences. They put us under a lot of pressure. It wasn't my best game, by a long shot, but I need to learn from it.
"I need to work out where I went wrong and, if I get another shot, try and be better.
"We've let ourselves down in terms of the performance."
Russell, Martin's team-mate at the Rams, is another player hoping to remain in coach Gordon Strachan's plans. He came on for the final nine minutes and played a part in Andrew Robertson's goal.
He said: "I've managed to get myself in. It's up to me to stay. I won't take anything for granted.
"I need to go back to Derby and if I can stay in the team and do well, hopefully I can get another call-up.
"I've loved it. I was meant to be coming as a fan so to get the call last minute and play a part tonight, taking away the result, it has been an amazing experience."
Watford's Anya admitted England were deserving winners.
"England were a lot better than us on the night in every aspect. They deserved their win," he said.
"We haven't played to anywhere near the level we've had over the last 18 months. We need to make sure it doesn't happen again, especially in future qualifiers."