Messi wasn't singlehandedly carrying but he had the most impact on the pitch for Barcelona. We also cannot deny the impact players like Xavi, Iniesta or Neymar had but Messi had the most impact. Before Neymar and Suarez joined, he had the duty of scoring goals and he did that very well. Even scoring 91 goals in a calendar year.
(I dunno how he did that) After Neymar and Suarez joined, he moved to the right flank and assisted them with tons of goals also while he scored lots by himself.
In my opinion, this is a biased statement - Xavi and Iniesta made the greatest contribution to the team. If you remember Xavi and Iniesta won the 2008 European Championship, then the 2010 World Championship and then again the 2012 European Championship - the greatest achievement. They did it without Messi, and without them, Messi himself failed at the 2010 World Cup and then at the 2011 America's Cup.
If you are solely talking about the 2010 WC, I have to say that compare the teams Spain and Argentina had. Yes, Argentina were a decent team back then but Spain National. the team was just far better. They had Iniesta, Xavi, Ramos, Casillas, and also the legendary David Villa and Fernando Torres.
So we should not be comparing the international achievements here.
If you wanna do so, look at what impact Messi had with this shit-current Argentian team. Without Messi, they are barely able to do anything. So, I could be biased but Messi has one of the most influence on both Barca and Argentina.