Gatland and Wales' preparation for the game was derailed by a potential strike by players over their dispute with the Welsh Rugby Union (WRU) that meant he had to cancel training sessions and delay naming his team.
They struggled to get a toehold in Saturday's match, and though they were within five points after 75 minutes until Ollie Lawrence's (23) try secured the win for England, they were always chasing the game.
"The week was challenging but we’re not making any excuses," Gatland said. "I think we can be critical of ourselves in terms of creating a lot of problems for ourselves by not being accurate in key moments.
"That’s what Test rugby is about. You’re in that arm wrestle. We’ve spoken about being hard on ourselves. I was pleased with some improvements."
Captain Ken Owens (36), who looked physically exhausted during the week as the negotiations with the WRU took precedence over match preparation, said: "The last two weeks obviously have taken their toll for a number of different reasons but we can't use that as an excuse.
"We spoke about the emotion of the last two weeks, we gave a massive effort for 80 minutes, we were right in the game throughout, but we left a couple of opportunities out there.
"Towards the end of the first half I thought we got on top and turned the ball over three or four times close to their line.
"I can't question the effort of this squad, we are in a rebuilding phase, we have got to rebuild pretty quick but the 23 who went out there today put out a massive shift."
Gatland made nine changes for Saturday's match after heavy defeats by Ireland and Scotland and has precious little time to try to work out his balance of keeping faith with the old guard who served him so well in his previous stint and bringing in fresh blood.
"Part of this Six Nations is about us thinking about the next six or seven months," Gatland said. "There are older players still holding their hands up and some younger players. We’ve not got that group in the middle. We’ve got to marry the two together."
