Manchester City took their unbeaten Carabao Cup run to 1,098 days in a near-stroll of a victory over a still-smarting Southampton. This was the Saints first game since Leicester trounced them 9-0 and it showed. They did, at least, lose by only two goals and achieve against Pep Guardiola’s side what they failed to do against the Foxes – score – but until City slackened off towards the end they were too tentative.

Relief for Marco Silva after Everton’s Holgate and Richarlison sink Watford Read more

Guardiola said: “We are already at the quarter-finals so we’ll see the draw. When you are in the semi-final or final you can start to think about that [winning it].”

For Ralph Hasenhüttl there was relief because he feared a repeat embarrassment. “Yeah – defending was the most important thing. It was a defeat but a reaction after a very difficult evening on Friday. To come here and play against one of the strongest sides on the planet showed the guys were committed,” he said.

“We were more passive in the first half but it was understandable after our last game. In the end it was important to show that reaction and that was the main goal for this game.

“Always when you come here, you never know what happens. Happy is the wrong word. I feel better than Friday but it was a very new and interesting case and with all the meetings we’ve had, I’ve found the right tone and it is important that they have shown they want to come back on the good track.”

Quick guide Carabao Cup roundup Show Hide Sunderland's Will Grigg and Marc McNulty both failed to convert from the spot as Oxford United won 4-2 on penalties after a 1-1 draw at the Kassam Stadium. Oxford, who dumped West Ham out after winning 4-0 in the previous round, led at the break through Rob Hall's effort before McNulty equalised for Sunderland with 12 minutes left. James Henry, Anthony Forde, Tariqe Fosu-Henry and John Mousinho all converted in the shoot-out for Oxford, while Grigg blazed his spot kick off target and McNulty's effort was saved. Colchester extended their run into the latter stages of the competition with a 3-1 win at League Two rivals Crawley, the first time Colchester have reached the quarter-finals of the League Cup since 1974. Dannie Bulman's curling first-half finish for Crawley was cancelled out two minutes later by Luke Norris's header. Michael Luyambula's own goal early in the second half gave Colchester the lead and Luke Gambin added their third. PA Photograph: Bradley Collyer/PA

Guardiola gave the 18-year-old Tommy Doyle his senior debut and selected Sergio Agüero and Gabriel Jesus – in a 4-3-3 – for the first time since last month’s 2-1 home win over Newcastle.

Hasenhüttl retained five from the Leicester thrashing – Oriol Romeu, James Ward-Prowse, Pierre-Emile Højbjerg, Jan Bednarek and Yan Valery.

Doyle, the grandson of the former City defender, Mike, played in the holding role. “He played well in a position that isn’t natural, usually he is further forward,” Guardiola said.

Facebook Twitter Pinterest Jack Stephens (fourth right) scores for Southampton on a right where they did claw back some credibility. Photograph: Nick Potts/PA

City fans taunted their opponents with a rendition of: “We want 10”. The challenge for City was one of trying to break down a team who held position around the edge of their area and after 20 minutes they succeeded. Doyle took a short corner to Bernardo Silva, he swung the ball in and Nicolás Otamendi moved between Romeu and Bednarek to head past Alex McCarthy from close in.

For Saints there was succour to be found in their having been 3-0 down at the same point against Leicester. And Guardiola was not totally content. More than once the manager urged his side to move the ball forward at pace rather than sluggishly and sideways. When Sofiane Boufal shoved Doyle over City had a free-kick 20 yards out. Agüero stepped up but his radar was awry and the ball sailed wide.

James Maddison makes Burton pay and helps fire Leicester into last eight Read more

Moments later there was no mistake, City’s second arriving as they upped the tempo. Jesus fed Silva who fed Riyad Mahrez and, when Kyle Walker overlapped along the right, his cross was volleyed expertly for Agüero’s 11th strike in 12 appearances this season.

City had been in low gear for most of the first half but still proved a class above their opponents. Saints, in damage limitation mode after Friday’s embarrassment, had shown close to zero intent, City enjoying 79% of possession.

The expectation was for more of the same after the break and so it proved with City controlling the game with ease. When high gear was engaged the Saints could do nothing about it. Agüero burst through the middle, flipped the ball to Mahrez and a reverse pass had Silva in but the winger was thwarted by a desperate McCarthy.

The Fiver: sign up and get our daily football email.

City’s only concern was the possibility a loss of concentration might allow a Southampton breakaway. Mahrez’s clumsy touch offered an example but the ball was claimed back and, seconds later, City had scored once more. Silva’s slick footwork left three defenders trailing before he found Mahrez. The Algerian saw his shot ricochet off Romeu and there was Agüero again to poke home from a few yards out.

Southampton were left to try to ensure three would not become four, or more. Mahrez went close when a close-range effort was blocked but the sense was a next City strike was on the way.

Hasenhüttl took off Boufal and Shane Long for Ché Adams and Nathan Redmond on 70 minutes and his team soon claimed a corner. Ward-Prowse took it from the right and Jack Stephens forced a save from Claudio Bravo. It was the defender who scored Southampton’s goal, heading past Bravo from another corner after Angeliño lost him.

But this was a canter to the quarter-finals for the holders and Southampton will hardly be looking forward to returning in the league on Saturday.