Sean Dyche looks on the bright side after Burnley are knocked out of the Carabao Cup by Manchester City
Barnes played 69 minutes - his first minutes for the first team since New Year's Day, following a hernia operation and furthe complications, while Tarkowski made his first start of the season after a toe problem, amid speculation surrounding his future.
West Ham had two bids for the centre back turned down, before Leicester City had one worth £30m knocked back on Friday.
Both clubs appear unwilling to go any further in their pursuit of the England international.
And Dyche said of the pair: "Barnesy was out there, which was good to see.
"He has had a long frustrating period but I thought he did really well.
"We only took him off as a precaution to make sure he continues on his journey back.
"And Tarky was out there, which was good.
"We want him to be here, he is a very good player and he will get fitter and sharper
"He said his toe was fine and I said the other day I trust him, and when he is ready he will let me know, and he did, so he played."
Dyche said: "Lowts has had to come off and we are going to have to wait and see on that tomorrow.
My first impression is that it is not deadly serious but we will have to wait and see because I have thought that about other players and they have been out longer than I thought.
"One of the physios said we can't really risk him playing, if it is sore then he has got to come off."
On the game, Dyche accepted his side were punished for giving the ball away too often in key areas: "We were playing a top side and they played a strong side which we thought they would.
"They hurt us on the critical moments like teams like that do.
"There were too many turnovers for us in critical areas."
But he felt Charlie Taylor should have had a penalty with the game goal-less, after being clipped by Fernandinho: "I can cry it in a little bit because I continue to struggle to see how we can't get penalties because there was two, certainly one out of the two if not two.
"I get told about these soft touches in the box and get given the insight of 'yeah but there was contact' and yet when our players get contact in the box apparently it is never quite enough contact.
"We get clear contact in the box and we can't get a penalty.
"But that doesn't mean that we win the game because these are a top class side."
Burnley may have lost 3-0, but keeper Bailey Peacock-Farrell shone on his home debut, making a string of saves: "I have said all along he is having a similar transition to Nick Pope.
"He is in the background and developing all the time. He has got a stature and has been working hard in the gym.
"I am pleased for him and he looked nice and sharp.
"It is an unfortunate thing for goalkeepers because he comes off the pitch 3-0 and yet he has played really well."