Besic was making his first appearance of the season for the Toffees, after injury had seen him miss much of pre-season as well as Everton's opening three Premier League outings.
The 22-year-old told Everton's official website the invaluable match fitness he gained from playing 90 minutes, plus extra time, will hold him in good stead as he continues his comeback from a stint on the sidelines.
"For me it was very important - I was really pleased that I played 120 minutes," Besic said. "In the last six months, that was only the second time I played over 90 minutes.
"Tonight was over 120 minutes and I was really tired after 60. But I was happy I got through the whole match.
"With the first goal and the third goal, when I am fit, I can stop those crosses and second crosses so, as you can imagine, I need more game time to get to 100 per cent.
"Now I want to play more but I have been injured for more than one month, so I have to respect that."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!