Steven Caulker was plunged into a Liverpool debut at centre-forward and in the ensuing chaos Christian Benteke made his one telling contribution against Arsenal to create a clinical equaliser from Joe Allen. With finales and cameos like that it is no surprise Jürgen Klopp claims judgment on his players must be reserved until the summer, although his actions reveal that process is under way.

There was no disputing Liverpool’s character on an enthralling night against the Premier League leaders or, in those dominant early exchanges when Roberto Firmino pierced the Arsenal defence seemingly at will, the ability that Klopp has yet to harness on a consistent basis from his side.

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That the Liverpool manager ended another game lamenting weak defending at set pieces, lapses in concentration and offering public support to Simon Mignolet, however, reinforced the sense that his work remains in progress.

But progress is being made in deciding who the manager can trust.

Klopp had stuck rigidly since October to the script of extolling the virtues of an inherited squad and insisting a major overhaul, and more expenditure from a club that spent around £80m on seven more players last summer, was unnecessary. Given the enforced search for a new central defender commenced in the Bundesliga and ended with Caulker arriving on loan from the Championship, there may have been more to Klopp’s stance than simply confidence-building. January’s budget is limited, although £5.1m has been committed to bringing Marko Grujic from Red Star Belgrade and Liverpool hope to clinch the pre-contract signature of Joël Matip from Schalke.

This week brought a departure from Klopp, however, with his admission at the Arsenal pre-match press conference that players will be judged worthy of his plans or otherwise at the end of the season. “It’s a contract for one year,” he said. “A very good season the player can leave, a very bad one and the club will let the player leave. Anything can happen.”

The only similarity between Liverpool’s starting line-up against Exeter City in the FA Cup and the Premier League leaders was in the grim news they heralded for Benteke. The £32.5m summer signing was included alongside the academy graduates and those summonsed from the wilderness (José Enrique and Tiago Ilori) against the League Two side on Friday. Against Arsène Wenger’s team, in keeping with all of Liverpool’s “big” games since Klopp took charge – Chelsea and Manchester City away – the Belgium international began on the bench and Liverpool’s attacking play was closer to what their manager envisages in his absence.

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Benteke’s reluctance, or inability, to read crosses into the area has been an obvious source of irritation to the Liverpool manager and Jordan Henderson berated the striker for hanging back when Jordon Ibe crossed along the face of goal in the second half against Arsenal. He would at least give a timely reminder of his aerial strength when steering Henderson’s cross onto Allen for the 90th minute equaliser.

As was the case at Stamford Bridge and the Etihad Stadium the Liverpool manager preferred Firmino to the former Aston Villa forward in attack and was repaid with a devastating display from the £29m recruit from Hoffenheim. Flashes of the Brazil international’s talent have been fleeting as he settles into the Premier League, and the occasional injury has not helped the process, but his quality was in evidence as he beat Petr Cech twice before the interval at Anfield.

Firmino provided the control and predatory instinct that Liverpool’s initial dominance required to open the scoring at Anfield. His exquisite second, swept into the top corner after Arsenal had twice failed to clear their lines, reflected the belief that was coursing through the home ranks at that stage and left Klopp throwing combination punches in delight. It only heightened the Liverpool manager’s despair that such excellence was deprived of its reward by weak defending that allowed the visitors to score with their first two attacks of the game. Olivier Giroud should have made it three from three only to somehow divert Theo Walcott’s inviting cross back into Mignolet’s grasp when connecting in front of an open goal.

Mignolet came in for more criticism from the Kop for his role in Arsenal’s first two goals and for a failure to connect with a Mesut Özil corner that almost found Per Mertesacker at the back post. Klopp appears to have decided that one Liverpool goalkeeper is out of favour, but it is not Mignolet. The Belgium international is close to signing a new five-year contract at Anfield but his understudy, Adam Bogdan, was dropped completely after conceding directly from a corner at Exeter. Danny Ward was on the bench against Wenger’s side having been recalled from a loan stay at Aberdeen and is the man most likely to put pressure on Mignolet until the end of the season.

With Ilori not even mentioned by Klopp when he listed his available central defenders on Monday, Benteke consigned to the bench for 66 minutes and Bogdan out of the frame, the manager’s purge is under way quicker than he is letting on. Defensive displays like this – and only Kolo Touré not being considered first choice from the side that started against Arsenal – hasten the process.