Frank Lampard was taking nothing for granted after seeing his Derby side move to the brink of clinching a Sky Bet Championship play-off place with a crucial victory.
A goal in each half from Tom Lawrence and Jayden Bogle against a City side reduced to 10 men for the final half hour mean that the Rams almost certainly need just one win from their last two games for a top-six finish.
However, Lampard said: "I see it that we need four more points. We have to expect Middlesbrough to win their remaining game so nothing is decided yet.
"The minute you switch off in this league it can bite you. We have to refocus quickly on the game against Swansea and hope we can keep the buzz in our dressing room going.
"It's a massive win against a very good team with a very good manager. We rode our luck at times, but we were due a game when things went our way.
"There were some really big individual performances. We spoke before the game about wanting to win more than them.
"That wasn't the case because they are a very honest team. But I thought we deserved the victory for our spirit and effort.
"It is a squad game and I thought substitute George Evans deserved special praise. He was man-of-the-match for me, although our goalkeeper Kelle Roos was outstanding as well."
Both teams lost central defenders to injury in the first half. Derby's Fikayo Tomori hobbled off on 11 minutes and was replaced by Evans, while City lost Nathan Baker on 33 minutes, Semenyo taking his place in a shuffled line-up.
Lampard added: "Fikayo has a dead leg and we will have to assess it further before knowing how bad it is.
"It was our first away win this year and there is a great feeling in the camp. But there is still work to do."
The visitors went in front on 18 minutes when Mason Mount penetrated City's defence on the right and passed to Lawrence, whose low shot took a wicked deflection on its way past Niki Maenpaa.
And the result was put beyond doubt on 77 minutes when a quick break saw substitute Mason Bennett feed Bogle, who fired into the roof of the net.
City were reduced to 10 men on 59 minutes when 19-year-old substitute Antoine Semenyo was sent off. The striker was shown a straight red card by referee Darren Bond for a lunging challenge on Tom Huddlestone.
The home side hit the crossbar in the second half through a volley from former Derby striker Andreas Weimann and were denied at times by some heroic last-ditch defending from Lampard's men.
Head coach Lee Johnson leapt to Semenyo's defence, saying: "The lad was on the wrong end of a poor decision. It was a booking at worst. He caught the lad with the follow through because he was stretching.
"He is very disappointed, but everyone supports him and he is a player we think has a big future.
"I couldn't fault any of my team today. They gave it everything and nine times out of 10 we would have won that game.
"It was just our finishing that let us down. That has happened before and it is something we need to address either by recruitment or player development.
"We are not giving up on our play-off challenge by any means. I think Derby have two very tough games left and, while that applies to us too, we will give it everything again at Millwall on Tuesday.
"If we play like that we can win our last two matches and anything can happen. Whatever division we are in next season there is a lot to build on."
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