A first half opener from Erin Cuthbert, converting the rebound after her penalty was saved, was followed by a second half header from substitute Martha Thomas as the Scots secured three points in the Spaniard’s first match in charge.
The visitors squandered numerous chances to make the scoreline more flattering but Losa was just delighted to get off the mark.
“I'm really proud of the guys' effort. We are very pleased in a lot of aspects,” he said.
On the number of chances his side passed up, he added: "Firstly we have to have the structure that we can create these opportunities.
"Key games in the past were decided on a lack of organisation. I'm very happy with the number chances we created. We deserved to score at least one or two more goals."
Scotland laboured in the first half despite taking the lead after 17 minutes when Cuthbert was brought down in the box, and although the Chelsea striker saw her penalty saved she followed up to turn home the rebound.
Scotland were dominating possession but they relied on goalkeeper Lee Alexander to keep their lead intact when she turned away a 30-yard effort Sipos at full stretch.
As half-time approached Jane Ross dragged an effort inches wide after a stunning ball through from Cuthbert.
Scotland upped the tempo at the start of the second half and a flurry of attacks ended with Kirsty Hanson’s low drive being tipped round the post.
Hungarian midfielder Vago almost gifted Scotland a second when she flicked a Cuthbert corner onto her own crossbar.
But the second goal duly arrived when Claire Emslie’s corner was glanced home by Thomas.
Emslie should have knocked home number three but when a Thomas cross presented her with a tap-in, she somehow put it wide.
Scotland now face the Faroe Islands at Hampden on Tuesday for their second World Cup qualifier and Losa is looking forward to playing in front of a home crowd.
"We play for our fans,” he added. “We play to make Scotland proud. The fans can make a difference in getting us qualification."