Manager Paul Hegarty apologised to the home fans for “an inept second-half performance” after Cowdenbeath hit back from a goal down to leave Montrose still searching for their first league win.
Hegarty said: “I was delighted to get a penalty just before half-time and Gary Fraser tucked it away well.
“When a team scores, that is when the opposition is most dangerous and we had to shut up shop.
“It was a good cross in between the centre-half and the right-back, but we had to stop it at source.
“You simply can’t legislate for mistakes like that which cost us the second goal and it cost us three points.
“Up until then, Michael Bolochoweckyj had been one of our better players.
“We have two points from five games and that is unacceptable…
“Since the Annan game we have had five good training sessions and I am flummoxed as to why my players failed to take their performance in training into the game.
“It makes Saturday (away to bottom club Edinburgh City) a six pointer just six games into the season.”
In a first half of few scoring chances, Montrose took the lead on 43 minutes. Gary Fraser was bundled over in the box by Nicolay Todorov and scored from the spot.
A minute into added time, Gary Glen dived to head home a Dean Brett cross.
On 54 minutes, a blunder by Bolochoweckyj allowed Glen to race clear and although Allan Fleming dived to parry his shot, Renton followed up to score.
The second half was as fragmented as the first and the closest Montrose came to a second equaliser was a minute into stoppage-time.
A Terry Masson shot came back off the crossbar and a follow-up header from Chris Templeman was saved on the line by David McGurn.
Cowdenbeath boss Liam Fox said: “We have not had the results I have been looking for, so I made a couple of changes.
“We have played better going forward, but we were more solid. We dug out the victory by doing the hard yards and winning the 50-50s. It was not pretty to watch. We cannot rely on our quality going forward and sometimes have to do the ugly side of the game.
“Our attitude and commitment was great, but that has to be a must every week.”