Clarke praised his players for overcoming fatigue and a slow start to ultimately seal a comfortable win against a team which finished with nine men.
And Clarke stressed his team still had a “realistic chance” of finishing top of their Nations League group despite Saturday’s 3-0 defeat in Dublin.
Scotland have six points at the halfway stage but face a double-header against World Cup play-off conquerors Ukraine either side of a Hampden clash with the Republic of Ireland in September.
Looking back at the four-game programme, Clarke said: “It was a difficult schedule for the players. It was difficult, but we haven’t made excuses until now.
“There’s no excuses for the two games that we lost. Two wins against Armenia are not going to make this international camp a good camp, because it wasn’t.
“We failed on our primary objective – to get to the World Cup. We failed on that and we had a really bad performance in Dublin, which put us on the back foot again. It’s nice to bounce back but there is work to do.”
Scotland had work to do after six minutes in Yerevan when they fell behind following Grant Hanley’s mistake.
Stuart Armstrong quickly levelled but Scotland looked vulnerable at the back until settling down around the half-hour mark.
The odds went in their favour just before the break when Arman Hovhannisyan was shown two yellow cards for fouling Nathan Patterson and headbutting John McGinn inside five seconds.
The visitors hammered home their numerical advantage with goals from Armstrong, John McGinn and Che Adams in the following 10 minutes of action.
Clarke, who revealed missing defenders Andy Robertson, John Souttar and Scott McKenna were “nowhere near” making the 2,500-mile trip, said: “We started the game slowly, there was a reaction to the long journey and the flight.
“There’s a lot of fatigue in the players’ legs that we haven’t really spoken about too much, because we don’t want to be seen to be making excuses. But it was there and they got in behind us and the players showed great character to come back.
“I’m delighted for Stuart, Che Adams and John McGinn – the three players we put in forward positions. It showed that our forward players can score goals.
“It was a game we wanted to win and a game we probably had to win, although not necessarily mathematically.
“It gives us the chance to go into the games in September with a realistic chance of topping the group and that’s what we wanted.”
Home boss Joaquin Caparros claimed the first red card was the deciding factor but Clarke said: “I thought we already had control of the game when it was 1-1.
“Don’t forget those challenges and tackles come as a result of us dominating possession, moving the ball quickly and playing quick one-twos. That’s a consequence of having control of the game.
“I understand what their coach is saying about the red card but you still have to capitalise and we capitalised just before half-time and then immediately after half-time, and the game was done after that.”
There were some angry scenes in the closing stages when Kamo Hovhannisyan was shown a straight red card following a wild challenge on substitute Lewis Ferguson and one home player had to be dragged away from Jack Hendry after the final whistle.
Clarke said: “To be fair to their coaching staff, they were on the pitch pretty quickly and made sure everyone was calm.
“Listen, there were some hard tackles towards the end of the game and professional players are always going to react to them.
“But it was nothing. I was more concerned about the bottles being thrown on the pitch after the tackle on Lewis. I saw one bouncing on the middle of the pitch, it was a hell of a throw.”