Former Hungerford Town boss Wilkinson took over from legend Gordon Bartlett, who managed the club for the last 22 years before deciding to step into a new role at the Stones.
There was little time for him to settle in ahead of two testing fixtures at Eastbourne Borough and then a home debut with Hemel Hempstead the visitors.
A late goal in both matches rescued a point for Wealdstone - highlights of Wealdstone's 1-1 draw with Hemel on Monday can be viewed here.
Wilkinson guided Hungerford to a sixth-placed finish last season and now begins a new challenge with the Stones.
After his first home game in charge on Monday, he told the club's website: "It was frustrating at times but we've ended up getting a draw so it's a stepping stone for us having lost the last two games at home.
"The way I look at it is that if you come from behind then you're showing character. There's got to be more belief but we've picked up two points this weekend so we've gained more points than some of the teams around us.
"We have a very good squad here, I'm happy with it but we've got a lot of work to do. They're fantastic lads, good players and we've just got to get that winning mentality in their heads. The minute we get that we'll be there or thereabouts.
"I have nothing but praise for the boys, we just need to believe a bit more. I believe in them and we need to start moving up this table and winning games, especially at home. I looked at the record, I think it's only 17 wins in the last three years so that has to be better if you want to be challenging at the top."