Manager Vincent Kompany applauded his side’s efforts for coming away from the Den with a point on Tuesday night despite conceding a late equaliser.
Ashley Barnes opened the scoring with his second goal in consecutive games in the second half before Millwall substitute Tom Bradshaw equalised in the 85th minute.
Speaking post-match in south London, Kompany praised his team’s performance and for coming away with four points from two difficult successive away trips.
Kompany said: “It doesn’t feel like a defeat. There were a lot of constraints before the game, we’ve had a few injuries, knocks and illnesses the last few weeks.
“So, to come here after the weekend and get a point and put in a good performance is good.
“It was a big test for us these last few days. To go to Luton and then Millwall and come through it with young players that haven’t tasted real English football yet.
“I just wish today we could have finished it off, but we’re not the finished article and there is work to do but I’m really pleased with the boys.”
Kompany added: "We want to win games, but we knew this was a really tough period in the calendar for us with Watford, Luton and Millwall back-to-back.
“Yet we've come through it. Four points from six out of those two games is good.”
Barnes grabbed his fourth goal of the campaign against the Lions and his second in just four days.
The Burnley boss hailed the striker’s recent performances and explained the influence the forward has.
“I’m pleased for him. I think he took the battle to them (Millwall) tonight.
“He had a great performance on Saturday and then another top performance tonight.
“Keep him fit, keep him happy and he’s been a big influence for us on and off the pitch this season.
“He’s really taken an opportunity and full credit to him for that. “ Said Kompany.