There are a few factors explaining why the Gospel was not proclaimed "into all the world", but it certainly was not because of disobedience from the Apostles. First, there are a few occasions we can read in the Gospels where the Apostles did not immediately fully understand what the Lord taught.
For example, Jesus plainly told them that He would be put to death and would resurrect the third day (Matthew 16:21; 17:23; 20:19 ; Mark 9:31; 10:34 ; Luke 9:22; 13:32; 18:33; 24:7, see John 14:26-28). Despite all that, the Apostles were still "astonished" that everything happened as Jesus said (Luke 24:20-22). Thomas even doubted (John 20:25)!
The Gospel was a totally new way of practicing worship to God (i.e. faith replacing works), and this was a difficult thing to grasp from the Jews' point of view, since they were under Moses' Law for many generations. If the Apostles, who were with Jesus and knew him on a personal level, were slow in understanding the Gospel, how was it for those who merely followed him, here and there? That being said, many people believed and accepted Christ anyway and, for this reason, there was much work among the Jews alone, and even if the Apostles and other disciples traveled themselves to spread the teachings of the Gospel, they also encountered many obstacles that slowed their progress down.
In Acts 6, we learn that the disciples worked hard, where they already were, and they spent a lot of their time ministering to the sick and the poor, and less on teaching. One could presume that they worried about the believers and continued to care much about the people who followed Jesus during His ministry. Thus why they organized special ministers for that, so the Apostles could spend more time spreading the Gospel to the Gentiles also, starting ~45 AD onward.
However, this was also about the time the persecution intensified. With the deaths of Stephen (~40 AD), then James (~45 AD). As pointed out, we know that the Apostles were commanded to expand the preaching to the Gentiles, as written in Acts 10, this is why Paul and Barnabas are called to serve missions unto the Gentiles, in 45 AD (Acts 13). Which did not go without persecutions either; Paul was stoned, but survived (Acts 14:19).
Today, this is odd because we do have all the writings somewhat chronologically, but most writings did not exist before 50 AD. Therefore we can assume that Peter was simply reminded to preach also unto the Gentiles, in Acts 10. And we know he promptly reacted to this vision.
Following the preaching to the Gentiles, many question arose and resulted in the Council of Jerusalem in 49 AD, regarding circumcision and other moral matters (Acts 15). Preaching to the Gentiles did not make things more easy to the Apostles, and it resulted in simply more persecutions, both from Jews as well as from Gentiles
The point is that, if the Gospel was effectively preached to the Gentiles, but did not extend much beyond the regions around Palestine (North Africa, Eastern Europe, Western Asia, etc.). Considering that nearly all the Apostles, including many disciples, were killed within 50 years after Christ's ascension is evidence enough of such persecution, and certainly did affect coordinating efforts in that sense. The destruction of Jerusalem, in 70 AD did not help either.
There would be other factors as well, but then my answer would become opinionated, and I will remain on the factual level. If I have missed anything, or did not fully answer the question, I will gladly update this answer.