The Tynecastle Park boss can be proud of his players who made it difficult for the home side for long spells with the second goal not arriving until stoppage time.
Here is how the Hearts players involved rated out of ten:
Ross Stewart - 8
The back-up goalkeeper put in his best performance in a Hearts jersey. Really calm with the ball at his feet and produced an excellent stop prior to the hour mark and then again in stoppage time to keep the score at 1-0.
Nathaniel Atkinson - 7
One of his better defensive performances as a right-back in a four. Was guilty of overplaying with the ball a couple of times but got the basics spot on from a full-back point of view, especially being up against arguably the best player in the league in Jota. Positioned himself well with crosses coming into the box.
Toby Sibbick - 6
Up until getting sent off for a daft second yellow card following a push on Liel Abada the defender had been solid, growing into the game at centre-back and then in the centre of midfield. Looks more at home in a back four than back three.
Kye Rowles - 8
A very, very good centre-back performance from a very, very good centre-back. Cut out crosses on a regular basis, cleared his lines. No nonsense and assured.
Alex Cochrane - 6
Caught out by Daizen Maeda for the opening goal, while he wasted set-piece opportunities with his deliveries. Solid enough in open play before getting sent off late on for two bookings.
Peter Haring - 7
A captain’s performance from the Austrian. A key defensive presence in midfield. May have been guilty of being loose with a couple of passes but produced some excellent challenges. Two arrived towards the end of the first-half, while he thwarted Celtic a few times in the second half. The type of role a midfielder needs to fulfil at Celtic Park.
Andy Halliday - 8
An excellent hour on the pitch before injury forced his substitution. Snapped into challenges, worked tirelessly alongside Peter Haring to protect the defence and also displayed his composure during a period after the break when Hearts caused Celtic some problems. Halliday was key to that.
Alan Forrest - 6
A selfless effort down the right-hand side. Was up against the bombarding runs of Greg Taylor, while trying to get back in and help Atkinson against Jota with Celtic favouring attacks down their left. Was able to show a bit more threat on the front foot after the break.
Liam Boyce - 7
Won some good flick-ons as the second striker behind Josh Ginnelly. Played a key part in Hearts’ best move of the game to help set up Josh Ginnelly for a great chance in the first half. Was removed, likely with Thursday in mind.
Gary Mackay-Steven - 6
Not much in an attacking sense and was guilty of being eased off the ball too easily on a couple of occasions. But was another player who bought into the collective of the team performance, carrying out his duties with discipline.
Josh Ginnelly - 6
Plenty of endeavour and ran his socks off to the point he was struggling to move at times towards the end of the game. Had Hearts’ best two openings, the first one he sliced well off target when he should have done better.
Michael Smith (7) replaced Andy Halliday and kept up the defensive protection and composure on the ball. Barrie McKay (6) and Lawrence Shankland (6) gave Hearts more quality in attack with the former producing a moment of excellence but Celtic started to dominate once more. Lewis Neilson (6) and Connor Smith (6) got valuable first-team minutes.