They went down 1-0, due to an own goal by Kerys Harrop, at Solihull Moors.
But that did not tell the whole story, as the new-look Blues carved out enough openings and opportunities to have probably won themselves.
But they just couldn't turn their play into something tangible, despite a number of first-half near misses and Chloe Arthur cracking a shot onto the post after the break.
"We would liked to have had more, of course," said Tejedor, Blues Manager.
"In some periods of the match I felt we played the better football. We created
"But if you are not able to score then you don't deserve to win."
Blues - with six new signings in the line-up - settled into the game after a while.
"It took us 20, 25 minutes to settle on the field," said Tejedor. "Then we played our best football in the second part of the first-half.
"Probably if they hadn't of scored so early in the second-half and we had reset and
continued as we had been playing, probably things would have been different."
The decisive goal came just 30 seconds after the interval, a factor that Tejedor was unhappy with.
"Very disappointing. We shouldn't have conceded that goal - an own goal - and
previously at the beginning of the action, we gave the ball to them.
"So when you get a couple of mistakes in a row, this is what can happen."
"I wouldn't say I'm happy," responded Tejedor, when asked if she was satisfied there were positive signs of how Blues want to play and what they want to achieve
"Of course, we are building our identity and I expect the players to defend our identity.
"But from that (performance), we know we need to get better."
She added: "There are always signs, even if you don't do things that well and lose.
"What your limits are, what you need to improve on . . . you learn a lot from a
game like this.
"It hurts. But it is a learning opportunity and we will look at what happened from
the point of view of getting better."
A major plus for Blues was the return of Rachel Williams, after a serious knee injury. She came on as a 55th minute substitute.
Williams has only had 45 minutes football in the past year, and that was for the Development Squad last weekend.
"She didn't play in the friendly matches. She is a great player. She gives us a lot. But she will need time as well."
* Blues Women can confirm that Tony Elliott has resigned as Goalkeeper Coach and joined Bristol City Women.
We would like to thank Tony for his time at the Club.