How to extract specific values with point coordinates from Kriging interpolations made in R?

By using R version 3.4.2 and the library "geoR", I made kriging interpolations for different variables (bellow I give an example of my process). I also made a matrix with the coordinates for 305 trees with distinct marks (species, DBH, Height) that are within the same space for the interpolations, as seen in the image attached (https://i.sstatic.net/NXghy.jpg). I've been looking for ways to extract the nearest value from each variable for each tree and save the corresponding values in a data.frame or matrix, but haven't been successful, and I can't find specific answers to this.

One thing I've been looking at is trying to convert the Kriging result into a Raster (.tif) and proceed from there. But Kriging interpolations are made out of vector data, so is it even posible?

I'd be glad to receive any sort of help, thank you in advance!

P.S. I'm doing this so that I can latter use the data for spatial point patern analysis.

#Kriging####:
PG<-read.csv("PGF.csv", header=T, stringsAsFactors=FALSE)
library("geoR")
x<-(PG$x)
y<-(PG$y)

#Grid
loci<-expand.grid(x=seq(-5, 65, length=100), y=seq(-5, 85, length=100))
names(loci)<-c("x", "y")

mix<-cbind(rep(1,10000), loci$x, loci$y, loci$x*loci$y)

#Model
pH1.mod<-lm(pH1~y*x, data=PG, x=T)
pH1.kg<-cbind(pH1.mod$x[,3], pH1.mod$x[,2], pH1.mod$residuals)
#Transform to geographic data
pH1.geo<-as.geodata(pH1.kg)
#Variogram
pH1.vario<-variog(pH1.geo, max.dist=35)
pH1.vario.mod<-eyefit(pH1.vario)
#Cross validation
pH1.valcruz<-xvalid(pH1.geo, model=pH1.vario.mod)
#Kriging
pH1.krig<-krige.conv(pH1.geo, loc=loci, krige=krige.control(obj.model=pH1.vario.mod[[1]]))
#Predictive model
pH1a.yhat<-mix %*% pH1.mod$coefficients + pH1.krig$predict
#Exchange Kriging prediction values
pH1.krig$predict<-pH1.yhat
#Image
image(pH1.krig2)
contour(pH1.krig2, add=TRUE)

#Tree matrix####:

CoA<-read.csv("CoAr.csv", header=T)
#Data
xa<-(CoA$X)
ya<-(CoA$Y)
points(xa,ya, col=4)

TreeDF<-(cbind.data.frame(xa, ya, CoA$Species, CoA$DBH, CoA$Height, stringsAsFactors = TRUE))
m<-(cbind(xa, ya, 1:305)) 
as.matrix(m)

I tried to find the value of a point in space (trees [1:305]) through the minimum distance to a predicted value using the following code, (I suggest not running this since it takes too long):

for(i in 1:2){print(c(2:10000)[as.matrix(dist(rbind(m[i,], as.matrix(pH1.krig2$predict))))[i,2:10000]==min(as.matrix(dist(rbind(m[i,],as.matrix(pH1.krig2$predict))))[i,2:10000])])}

Solution

In the following link aldo_tapia's answer was the approach needed for this problem. Thank you to everyone! https://gis.stackexchange.com/questions/284698/how-to-extract-specific-values-with-point-coordinates-from-kriging-interpolation

The process is as follows:

Use extract() function from raster package:

library(raster)

r <- SpatialPointsDataFrame(loci, data.frame(predict = pH1.krig$predict))
gridded(r) <- T
r <- as(r,'RasterLayer')

pts <- SpatialPointsDataFrame(CoA[,c('X','Y')],CoA)

pH1.arb <-extract(r, pts)

to this I just added the values through cbind to the tree data frame since they are in order.

COA2<-cbind(CoA, pH1val=pH1.arb)

I will repeat the process for each variable.