During their stay in Austria the Celtic boss has watched his side defeat Krasnodar and LASK Linz either side of drawing with Rapid Vienna.
But the new boss spotted flaws in the performances - and has let his Bhoys know what must be improved.
In their last game before the Hoops take on KR Reykjavik - who lost 2-0 in the league at bottom club Thor last night - in their opening Champions League qualifier on Tuesday, Deila wants confirmation his players can deliver what he demands.
Places in the line-up for Iceland are on the line, and the Norwegian made it clear the step up in performance he asked for and got between drawing with Rapid and defeating Linz must be repeated.
He said: "The Rapid Vienna game wasn't at the level I wanted, but on Tuesday I was satisfied. I'm looking forward to the game tonight as I think we are taking steps every day."
Deila rested several first-team regulars in the 5-2 win over Linz, and told Celtic TV: "I was happy we kept compact for 90 minutes, and that we looked more comfortable on the ball.
"We didn't lose as many balls as we did in the game before. But still the passing and the movement need to be quicker, and that we have to work on."
Deila has enjoyed watching some of the younger players grabbing the chance to impress, and Liam Henderson - despite collecting two yellow cards against Linz - was singled out for special praise.
"He is a big talent, and we are going to take very good care of him," promised the manager.
"He works the right way, with motivation to be better every day."
"We have a lot of players who are very good, but have been out with injury for a long time, so they need time to get up to fitness."
One man back to bolster the side, and hoping to take part in tonight's game, is Emilio Izaguirre.
He only met his new manager for the first time when he joined up with the squad at the start of this week, having endured an unhappy World Cup with Honduras.
Despite his extended season, the full-back feels fresh and ready to go.
Deila's preference is for his full-backs to get forward and deliver crosses for the strikers.
This plays to Izaguirre's strengths and he told the club's website: "I like to attack and run forward, but the most important thing is that the team does well.
"There is a lot of competition at the club as the new manager wants to improve and wants to see the players do better.
"This is good for competition, and we have great quality in training.
"Since 2010, I have worked hard and tried to improve in every game, and this year I want to continue doing that and also try to score more goals."
Izzy - signed by Neil Lennon following his showing at the 2010 World Cup finals in South Africa - has embraced the new training regime and said: "I've enjoyed it.
"The football has changed in some ways, but I'm happy about that.
"Every manager has different ideas about training, and all my team-mates tell me this manager has made big differences in the match play and in training. This is good for Celtic."