The world number seven crashed out in Birmingham after a 6-1 6-3 loss to the American, a grass-court specialist who reached the fourth round at Wimbledon last year.
Konta was beaten in the final of the Aegon Open last week by Donna Vekic as she failed to take the opportunity to win a first title on home soil.
And Konta does not believe the early exit in Birmingham is a blow to her build-up to Wimbledon and said: "Me losing second round against a very good player on this surface is by no means a blow. It's part of the game.
"Just because I am seven in the world does not mean I am entitled to winning every single match. My job is to go out there and do the best that I can.
"Point being that I think I actually played two good matches here. I played a very good first round against someone who made semis last week in Hertogenbosch. I think I played a great match there. I think last week I played five great matches. I lost to a player who played better than me on the day."
Konta won only 11 points as she lost the first set inside 24 minutes and although she improved in the second set fell to defeat in 64 minutes.
Vandeweghe faces Spain's Garbine Muguruza in the last eight after her 6-1 6-4 win over Alison Riske.
Fifth seed Kristina Mladenovic edged into the quarter finals after a 6-4 7-6 (7/3) win over China's Zhang Shuai.
Elina Svitolina may decide to skip Wimbledon because of a foot problem after the world number five was knocked out by Camila Giorgi.
Svitolina has been one of the form players of the season but has only ever won two matches at Wimbledon and does not want to jeopardise her chances of success on hard courts.
The Ukrainian said: "I'm disappointed I'm out of the tournament, but not disappointed about my performance because I couldn't really show even like 50 per cent of what I can do.
"I was really looking forward to this year at Wimbledon. But today the court was slippery and it's so bad for my foot.
"I will do my best. But for the moment it's very uncomfortable, and there is a question, I think, about it, because the season is still long and there is lots of big tournaments as well where I will feel more comfortable and confident on the hard court."
Svitolina started the Aegon Classic as the highest-ranked player following the withdrawal of world number one Angelique Kerber, but the second seed was out-hit by Italian qualifier Giorgi, who triumphed 6-4 4-6 6-2.
Giorgi, ranked 102, moves through to a quarter-final clash with Australia's Ashleigh Barty.
