United moved into the League Cup quarter-finals after goals from Christian Eriksen and Marcus Rashford either side of half-time sealed victory.
“I think after a break it’s always difficult to find the rhythm but I think we did quite well,” Ten Hag said.
“Also, some different players came on and I think they played quite well. I had a routine (and it wasn’t) 100 per cent, but you see that the principles are there and I am quite happy with the game we played.
“There is definitely room for improvement, we have to work on that, but of course I am pleased with a win.”
One player who impressed the Dutchman was off-season signing Casemiro who put in a full shift in defence.
“What you can expect: really experienced, really composed,” Ten Hag said. “He was leading a good combination with Victor Lindelof. So I was happy with the performance.”
Rashford also earned praise, backing up after scoring three goals at the World Cup.
“I think he was a threat for the defending line of Burnley,” Ten Hag said. “He moved so often behind the defending line and they are the most difficult situations to get the ball there.
“But with the passing capabilities of players like Eriksen, Casemiro and Bruno, we have the players that can get the ball there. (You have to) keep going and keep believing that the ball is going to get there, but it is an investment.
“Costs a lot of energy and costs a lot of power and today he got the benefit from it. It was a dribble and a great goal.”