The rookie Ibrox manager has successfully negotiated his first test after guiding his side past opening Europa League opponents FK Shkupi.
But there was not much to get excited about following the 2-0 aggregate win as Rangers laboured to see off their Macedonian opponents.
First-leg goals from Jamie Murphy and James Tavernier at Ibrox gave Gerrard’s side a crucial advantage but the former Liverpool and England captain has warned his shot-shy strike force to sharpen up after watching them draw a blank in the Skopje return.
However, chairman King insists he is encouraged after watching Gerrard’s new-look defence open the campaign with back-to-back clean sheets as they saw off a repeat of last year’s humiliating first-round exit to Luxembourg no-hopers Progres Niederkorn.
And he believes Rangers will only get slicker going forward as the weeks go by.
In a pre-season address posted on the club’s website, the South Africa-based businessman told supporters: “It was pleasing to see the new squad settling down with the successful navigation last night (especially after last year) of a potentially tricky Europa League fixture with two clean sheets to the players’ credit.
“On this point, I am conscious that we were top scorers in the SPFL last season but conceded far too many goals to be able to finish higher than third.
“This leakage will be much reduced in the coming season thanks to the efforts of (director of football) Mark Allen and Steven in the transfer market.
“This team will continue to improve which makes me more relaxed for this coming season than I have been for any since regime change.”
Champions League-winner Gerrard was appointed back in May but only after youth coach Graeme Murty was placed in charge for a six-month spell as King and his board went in search of the right man to replace Pedro Caixinha.
That delay was roundly criticised but King remains adamant it will eventually prove to be the right course of action.
He added: “I made it clear in prior statements that your board will always act in the long-term interests of the club and not be influenced by a minority of vociferous supporters, or members of the media who continuously attack our club.
“This was never more evident than in the appointment of our new manager - Steven Gerrard. We were constantly put under pressure to make an appointment even though we did not consider the available candidates to be suitable to take the club forward.
“We had many candidates with managerial experience, but the experience was not necessarily successful or of the standard that we felt we needed - particularly given our desire for stability after our recent experience of manager changes.
“We resisted the pressure and made an appointment only when we felt that we had an outstanding candidate that we could support.
“We ultimately appointed a man whose football pedigree, knowledge, character and winning mentality is unquestioned and we will back him while he gains management experience. A winner is a winner.”