Tommy Wright took plenty of encouragement despite starting his Kilmarnock reign with a home defeat at the hands of Motherwell.
Allan Campbell's 71st-minute strike earned Well a 1-0 win which moved them four points above Killie in the Scottish Premiership and inflicted a sixth straight defeat on the hosts.
Motherwell striker Devante Cole had a series of chances before the goal but Killie enjoyed the bulk of possession and pressure with Nicke Kabamba failing to make the most of a good headed chance in stoppage-time.
The visitors defended their box well to claim a first clean sheet under Alexander and Wright saw enough attacking intent to give him hope following his first three days in the job.
"Most certainly I'm encouraged," he said. "I have been encouraged since I came in with the quality in the squad. We will work with them. We know the areas we have to improve and they just have to persevere with it."
The former St Johnstone boss added: "I think we bossed possession. We worked on getting the ball into wide areas and creating overloads in those areas to get balls in the box.
"We did that and had numerous attempts on goal but the quality of those those attempts didn't trouble the goalkeeper enough.
"Ultimately, though, we have just been caught as so often happens when you are in the run we're in. It was a quick throw and we lost our shape a little bit.
"At no stage of the game Motherwell cause us a problem from open play but they have won the game and Graham will be a happier manager than me. His side have defended well. The two centre-halves have won everything going into their box."
Motherwell took the lead when Tony Watt collected a quick throw and split the Killie defence with a pass that set up Campbell to lash the ball in off the bar.
Alexander said: "It was a brilliant three points and I'm delighted with a clean sheet for the first time in a while.
"It was a grind at times with both teams really competing.
"Kilmarnock were very well organised and they were hard to break down. We had to do all the basics well and I thought we did that.
"We were just striving to find that bit of quality and thankfully Allan Campbell found it. It was a great turn and pass from Tony Watt but what a finish from Allan."
