The Bundesliga side dominated possession and Mladen Krstajic headed the only goal from a 30th-minute corner.

Rangers were without striker Kris Boyd, who suffered a minor hamstring problem, and rarely threatened the German side.

But Smith was content with their eight-day spell on the continent, which also included two victories over lower-league German sides.

The Rangers boss said: "It was a good workout for us. Obviously with the standard of team Schalke are, it was always going to be difficult for us.

"They had more good possession of the ball, as you would expect from them when they are at home.

"In the first half, we were disappointed to lose the goal in the manner we did from a set-play but I don't think we could complain as they deserved their lead at that time.

"Schalke have had good results here and this is a difficult place to come. They've been in the top four in the Bundesliga for the last few seasons.

"They've had decent results in the Champions League as well. They're a good team and they gave us a good test at the end of our pre-season build up in Germany.

"It is always difficult at the end of the week because there is a little bit of tiredness in the legs and our play.

"But it has been a good trip for us because we have done a lot of intensive training as well as playing games."

Rangers came close to snatching an unlikely draw when late sub Andrius Velicka came close to his first goal for the club following his move from Viking Stavanger when his diving header struck the post.

"I thought Andrius played well, as he did the other night when he came on against Sportfreunde Lotte," Smith said.

"We have been happy with him, although we should remember he has a bit of a head start on the boys.

"He has been playing for a period of time now in Norway and I think that shows up a little bit."

Rangers have lost Kyle Lafferty, Steven Smith and Barry Ferguson to injury for their first Champions League qualifier, almost certainly against Kaunas, on July 30.

Carlos Cuellar has also been left out of their three matches because of a calf problem and Smith decided not to risk Boyd this afternoon.

"We've had one or two problems on the injury front this week and it has been frustrating as Kris now has a hamstring injury," Smith told www.rangersfc.co.uk.

"It is actually just tight and, like a lot of the boys at the present moment, we felt as though it was better not to put him under the pressure of games.

"When we look back over last season and the amount of games we had, things are bound to take their toll a little but once we get up and running, I'm sure we'll be okay."