Burnley had a 2-0 lead at halftime, but United clawed back a point at Old Trafford.
“There is nothing other than pride in what we've achieved today," Dyche said. “The squad is at stretch and I've spoken many times about my belief in the group and that was on show today.
“On the back of an awkward game (against Spurs) the other day, it's a fantastic point because it's very difficult to come here.
“They've only lost to Manchester City and not dropped another point, but we made a great start and got in among them.
“In the second half we had to dig in and that's what you have to do at these grounds, so overall, it's hard to be disappointed after scoring two goals at Old Trafford and taking a point."