The 19-year-old was used extensively by Aidy Boothroyd during the recent international break.
The midfielder played the full game against both Georgia and Spain and was brought on as a substitute for the final 23 minutes against Greece as the team secured their qualification to the European Championships this summer.
And while Evans insisted that he was not pleased with the amount of time Cook was on the pitch for the Three Lions, he conceded that had he been in Boothroyd's position, he would also have looked to pick the youngster as often as possible.
"It's disappointing that he played so much because we made a request for them to limit his games but I've known Aidy for years, he's a good coach, and in fairness to him his priority was getting the England squad to the finals," he told the Yorkshire Evening Post.
"It's a big deal for them, as it will be for Cooky, and in Aidy's position I'd probably have done the same. As a club we're just trying to look after him and to make sure he doesn't get pushed harder then he should."
Although Evans would have been encouraged by Cook's performances in the three games - as England went unbeaten, winning both of the games the 19-year-old started - the fact that he dropped him to the bench for the club's most recent encounter after claiming that he was exhausted following the fixture before that would suggest that he is looking to manage the player's workload heading into the final part of the campaign.
While Leeds' season is practically over in terms of either getting promoted or relegated, Evans appears to be in serious danger of losing his job in the summer (via Daily Mail), so may be relying on his team to put in a string of good performances before the end of the campaign to help his cause, and give them some momentum heading into next year.
And with Cook already establishing himself as one of the key men in the team, making sure that he is at his best physically could go a long way to making sure that he has the maximum impact on the games he plays, which may be why he was hoping that he would feature much less often for the national team.